0000223482 00000 n Q 0.562 0.087 TD 0.015 w q >> /F1 0.217 Tf 0 g Q 0.165 0.129 m Q q /Type /XObject 45.324 0 0 45.147 54.202 460.721 cm Q >> q S Q W* n >> Q stream /Font << Q q /F1 0.217 Tf /FormType 1 /Font << endobj >> endobj /Length 55 q BT 0.314 0 l 0.458 0 0 RG >> /Subtype /Form Q 221 0 obj << 45.249 0 0 45.527 217.562 491.586 cm /Meta824 Do Solve using the quadratic formula: a) EMBED Equation.3 =EMBED Equation.3 EMBED Equation.3=EMBED Equation.3 ; a = ____, b = ____, c = ____ EMBED Equation.3 EMBED Equation.3 Worksheet 35 (7.4) EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 The solution set is ____________. 0 G /Length 562 q /Meta460 475 0 R stream /Length 34064 /BBox [0 0 0.413 0.283] Q Q q Q 0.458 0 0 RG Q /Meta89 Do /Length 76 W* n >> Q 1 g Q 0 w >> >> /Length 76 /Matrix [1 0 0 1 0 0] 45.249 0 0 45.527 329.731 468.249 cm 0.031 0.437 TD 0000188539 00000 n q 1070 0 obj << 0 0 l /Matrix [1 0 0 1 0 0] /Meta74 Do /I0 Do 0 w /Font << W* n q 0.015 w q /Subtype /Form >> Q /Font << 0000227897 00000 n stream /FormType 1 /Type /XObject Q Q endstream q q /FormType 1 /Matrix [1 0 0 1 0 0] q Q 1 J stream >> 0.267 0.283 l 0.566 0.366 l /Resources << Q endstream q 0 G 0 0 l W* n stream /Length 55 /Matrix [1 0 0 1 0 0] /F1 6 0 R 578.159 506.642 l Q /Font << /BBox [0 0 9.523 0.633] q q 0 G >> 0000176178 00000 n endobj 0 0 l 0 g 278 0 obj << [(-)] TJ 0 g /Length 55 >> /Subtype /Form q 916 0 obj << /I0 Do 3 1. q 45.249 0 0 45.147 329.731 86.573 cm q endstream 0.015 w stream endstream 0 0 l Q stream /Matrix [1 0 0 1 0 0] 0 G [(B\))] TJ /Subtype /Form W* n ET 0 0 l q q 45.663 0 0 45.168 426.844 362.102 cm 0000064394 00000 n BT /Meta128 Do Q 45.249 0 0 45.131 217.562 216.057 cm /Type /XObject /Matrix [1 0 0 1 0 0] 0.458 0 0 RG 0 0.283 m /Matrix [1 0 0 1 0 0] /Meta1051 Do /Meta1038 1055 0 R /Matrix [1 0 0 1 0 0] 45.249 0 0 45.147 329.731 107.652 cm q /FormType 1 0 0 l 0.001 Tc /Resources << 0 0.283 m Q ET /FormType 1 /Resources << /Resources << /Meta8 Do /Meta836 851 0 R >> /Length 61 0 g /Font << 0000052488 00000 n BT q Q /Matrix [1 0 0 1 0 0] ET endobj >> 0 0 l endstream /Length 55 ET q /F1 6 0 R q /Font << 0 0.087 TD 45.249 0 0 45.413 329.731 263.484 cm /Type /XObject 0 G /Resources << stream /Type /XObject Q stream q 0000055059 00000 n 0000196274 00000 n 0.031 0.087 TD We took this picture on the internet we think would be probably the most representative pics for Dividing Complex Numbers Worksheet. /Subtype /Form Q 0.267 0 l Q /Meta1073 Do >> 0.267 0 l Just in case you forgot how to determine the conjugate of a given complex number, see the table … Dividing Complex Numbers Read More » 0000168862 00000 n /F1 0.217 Tf Q 0.015 w 0 g q 0000043878 00000 n /Subtype /Form stream /Font << /Matrix [1 0 0 1 0 0] q >> BT stream /Font << q BT /Length 94 0 g /Subtype /Form /FormType 1 0.748 0.308 TD Q 0.458 0 0 RG endobj /Subtype /Form /Length 102 /Meta174 185 0 R q >> 0 G /Matrix [1 0 0 1 0 0] /Font << 0.001 Tc Q /Font << 1056 0 obj << /FormType 1 /Length 55 /Type /XObject Find the dimensions of the plot of ground if the area including the sidewalk is 819 square meters. endobj /FormType 1 /FormType 1 /Matrix [1 0 0 1 0 0] 0.267 0 l /Meta718 733 0 R stream /BBox [0 0 1.547 0.33] 1.547 0.633 l /F3 0.217 Tf q /Meta842 857 0 R /FormType 1 BT endstream 45.663 0 0 45.168 202.506 362.102 cm /Matrix [1 0 0 1 0 0] /F1 0.217 Tf Q 0000100512 00000 n endobj endobj /BBox [0 0 9.523 0.633] /Meta328 341 0 R 1.547 0 l 1 g q 550 0 obj << q 9.791 0.283 l S q /Matrix [1 0 0 1 0 0] 9.523 0 l 0.564 G /Length 102 /FormType 1 /Subtype /Form 0 0.283 m 941 0 obj << 0.381 0.087 TD /BBox [0 0 1.547 0.33] /Meta975 990 0 R Q 0 G 45.214 0 0 45.147 81.303 691.834 cm 0000168630 00000 n >> /FormType 1 0 0 l q /Length 63 >> /FormType 1 W* n 45.527 0 0 45.147 523.957 254.45 cm 11.988 0.283 l /F1 0.217 Tf /Meta546 Do /Length 8 BT >> /Type /XObject /BBox [0 0 1.547 0.283] 0000057576 00000 n Q /Subtype /Form In Exercises 67-8, divide and simplify into the form a + bi. /Type /XObject /F1 0.217 Tf 0 g /Length 102 stream 877 0 obj << Q stream 781 0 obj << 0000079638 00000 n /FormType 1 q /Subtype /Form /Resources << -0.005 Tc q 349 0 obj << /Length 53 /F1 6 0 R Q Q 0 g /Matrix [1 0 0 1 0 0] /Length 53 /Meta154 165 0 R /Meta560 575 0 R 0000259541 00000 n >> Q /Meta640 Do /Meta110 121 0 R /Meta495 510 0 R q 0.232 0.308 TD 286 0 obj << /Font << 0.564 G 0.267 0.283 l 45.249 0 0 45.413 105.393 513.418 cm Q /Meta502 Do 1 j W* n 0.015 w 45.249 0 0 45.527 217.562 535.249 cm >> Q /Meta475 Do 0 g /Meta874 889 0 R Q Q /Resources << 0 g >> 0 G 0 0.283 m /FormType 1 q /Meta513 Do 0 G /Subtype /Form 0 G Q endobj /F1 0.217 Tf >> q 0.458 0 0 RG /Subtype /Form 0.564 G q endstream /Type /XObject q >> 45.214 0 0 45.131 81.303 317.686 cm 45.663 0 0 45.147 426.844 203.259 cm 0 g >> /Resources << stream /Meta564 Do endstream 45.663 0 0 45.168 202.506 216.057 cm /Length 64 Q W* n /Meta1049 Do /Meta397 Do >> /Font << 330 0 obj << Q /F1 6 0 R /Font << /Resources << 0 w >> /FormType 1 /BBox [0 0 1.547 0.283] /Meta116 Do 45.249 0 0 45.413 441.9 263.484 cm >> >> >> 0 0.283 m 9.791 0 l q q Q Q stream 9.791 0 l /Length 67 W* n /F1 6 0 R [(i)] TJ 0 G /Meta278 Do >> stream /Matrix [1 0 0 1 0 0] 0000268293 00000 n >> endstream (3 + i) - (9 + 4i) Worksheet 38 (7.1) Summary 3: Multiplying complex numbers: 1. Q 538.26 528.474 m endstream stream 0000091531 00000 n stream /Meta162 173 0 R /Length 102 0000065556 00000 n Q q /BBox [0 0 9.523 0.33] 1.547 0.33 l Q Q /Font << Q 0 0 l q /Meta951 Do >> /Meta1060 1077 0 R Q /BBox [0 0 11.988 0.283] [( 2)] TJ 0 g endstream Q /Length 102 45.249 0 0 45.131 217.562 289.079 cm 0 g /Matrix [1 0 0 1 0 0] ET 0 0.087 TD 0 G q /Resources << 0000066019 00000 n ET Q /F3 21 0 R /Type /XObject stream /Matrix [1 0 0 1 0 0] 1 J q 45.213 0 0 45.147 36.134 746.037 cm /Meta234 Do ET 0 g -0.008 Tc /FormType 1 q 0 g /Matrix [1 0 0 1 0 0] /FormType 1 >> /Meta1061 Do /Matrix [1 0 0 1 0 0] /Length 8 BT >> Q /Font << /Length 55 0 0 l q /Length 102 45.249 0 0 45.413 217.562 558.586 cm /Resources << Q 0 0.283 m /Font << /Matrix [1 0 0 1 0 0] 45.214 0 0 45.147 81.303 550.305 cm /F1 0.217 Tf >> 0000348859 00000 n /Meta295 308 0 R 0.458 0 0 RG /FormType 1 0.458 0 0 RG q [( 8)] TJ /Font << q 45.214 0 0 45.147 81.303 550.305 cm /Widths [ 493]>> W* n 0.015 w 1.547 0.633 l ET /FormType 1 /Meta610 Do endstream q 0 0.5 m 1.547 0.283 l 0.283 0.087 TD >> W* n endstream /F1 0.217 Tf 0 g BT 45.249 0 0 45.147 105.393 679.036 cm endobj Q W* n Q -0.002 Tc /FormType 1 0000092412 00000 n 45.663 0 0 45.147 314.675 263.484 cm 284 0 obj << /Length 65 endstream 1 g /Font << /Type /XObject /FormType 1 45.249 0 0 45.131 329.731 143.034 cm /Meta287 300 0 R endobj q /Type /XObject /Meta633 Do 0 G q >> 0 w /Font << >> endstream /Subtype /Form q 0.458 0 0 RG ET /Meta713 728 0 R endstream /Meta969 Do 863 0 obj << /Matrix [1 0 0 1 0 0] 0 0.366 m /BBox [0 0 0.263 0.283] 0 g /Meta1067 1084 0 R q /Type /XObject 813 0 obj << 0 G /F3 21 0 R endstream /Length 303 /Meta276 Do ET /Type /XObject /Meta822 837 0 R /Matrix [1 0 0 1 0 0] Q /Matrix [1 0 0 1 0 0] 45.249 0 0 45.147 441.9 107.652 cm 0 G Q 0000181812 00000 n q /BBox [0 0 1.547 0.33] Q /I0 36 0 R /Length 67 /Resources << /BBox [0 0 1.547 0.283] 0.031 0.087 TD /Matrix [1 0 0 1 0 0] >> Q stream Write an appropriate solution set. /FormType 1 /Resources << Example - ˇˆ˙ ˝˛˚˙ = ˇˆ˙ ˝˛˚˙ ∙ ˝ˇ˚˙ ˝ˇ˚˙ (Multiply by complex conjugate) = ˇ˝˜˙ˇˆ˙ˇ˝˚˙ ˝ˇ˚˙˛˚˙˛˚ ˙ = S Q 0000004657 00000 n /F3 0.217 Tf 0 0.283 m 11.988 0 l /Meta649 Do endobj -0.007 Tc 335 0 obj << q 45.663 0 0 45.147 314.675 622.575 cm W* n >> q BT endstream endobj q q 1.547 0.283 l >> 0 g Q endobj endstream stream >> 45.214 0 0 45.147 81.303 550.305 cm 45.249 0 0 45.527 217.562 491.586 cm 0.267 0 l 0 g Q # � : � z � � � � � 0000357105 00000 n /Meta952 Do Q 0.267 0.283 l endobj endstream 1 j /BBox [0 0 1.547 0.283] 0000050673 00000 n /Meta818 833 0 R /FormType 1 1 g q q q ET Q /Length 562 /Meta1064 Do Q q [(i\))] TJ 45.663 0 0 45.147 202.506 298.866 cm /Matrix [1 0 0 1 0 0] /Meta870 885 0 R q q /FormType 1 0.015 w /Subtype /Form q endobj Click here to buy the accompanying White Rose Maths workbook. q 0 0.633 m /Meta175 Do /Font << q /Type /XObject endobj q >> /BBox [0 0 9.787 0.283] endobj 976 0 obj << 0 0.283 m q 445 0 obj << W* n endstream /Meta278 289 0 R /FormType 1 /FormType 1 0 0.283 m /Subtype /Form /Length 55 >> Adding in standard form. q /Meta60 Do 0 0.283 m /Type /XObject /Meta472 Do Q 0.381 0.087 TD 0000257752 00000 n >> 0 w /Meta262 273 0 R /Type /XObject /BBox [0 0 1.547 0.633] endstream BT ET 0.564 G -0.008 Tc stream 0 g q 0.5 0.087 TD 0 G 0.381 0.087 TD Q /FormType 1 45.249 0 0 45.413 105.393 263.484 cm /Subtype /Form 1 g /Length 66 Q 45.249 0 0 45.131 217.562 289.079 cm /Meta503 518 0 R /BBox [0 0 0.263 0.283] /Length 55 1112 0 obj << /Type /XObject ET Q /MediaBox [0 0 614.294 794.969] /Type /XObject 0.531 0.158 TD BT 0.232 0.308 TD /FormType 1 6.157 0.087 TD /F1 6 0 R q BT >> 45.413 0 0 45.147 523.957 629.351 cm stream Q /Meta241 252 0 R /FormType 1 /FormType 1 /BBox [0 0 1.547 0.33] 0.267 0.5 l q Q 11.988 0.283 l stream Q 0.417 0 l /Subtype /Form 0 G Q 0 g 45.249 0 0 45.131 217.562 216.057 cm 0000244579 00000 n /Resources << [(B\))] TJ 1 g 0 G /Meta109 120 0 R >> q >> 0.001 Tc stream q Q 0.681 0.366 l 45.663 0 0 45.147 314.675 718.183 cm 0.216 0.165 l 45.249 0 0 45.131 441.9 143.034 cm >> Q >> /FormType 1 0 g /BBox [0 0 11.988 0.283] /Type /XObject 0 0.087 TD q 45.249 0 0 45.527 217.562 535.249 cm /Subtype /Form EMBED Equation.3 3. /Subtype /Form endobj endobj q 0 G ET 0.564 G 0 0.283 m >> /Subtype /Form 0 0.283 m 0.531 0.283 l 0.712 0.087 TD /Type /XObject Q q BT 0 w ET Q /F3 21 0 R endstream /Type /XObject 0.015 w q /Length 136 BT /F1 0.217 Tf 0 0 l /Meta646 Do q endobj 0.015 w q /F3 21 0 R ET 241 0 obj << >> q /Meta1049 1066 0 R /FormType 1 [(-)] TJ endstream /MissingWidth 252 1.547 -0.003 l [( \()] TJ Q 1 g Q 0 0.283 m W* n /FormType 1 45.249 0 0 45.147 441.9 718.183 cm endobj ET 0000356616 00000 n 0 G Q 0 w ET 0 0.283 m /F1 6 0 R /Meta155 Do 0 g 0.267 0.5 l 0 0.283 m q 0 w 1 g q Q 1 J /BBox [0 0 0.531 0.283] stream /Meta710 725 0 R Q Q endstream BT 563 0 obj << Q Q /Meta1058 Do 45.249 0 0 45.527 329.731 491.586 cm /Meta282 Do q 1.547 0.33 l /Meta1048 1065 0 R 0 w 0 G Q 0 G /BBox [0 0 9.523 0.283] /FormType 1 0000177881 00000 n /Resources << Q q 0000147904 00000 n /Font << 0 0.283 m 0 g /Matrix [1 0 0 1 0 0] >> stream /Meta377 390 0 R Factor all numerators and denominators completely. 623 0 obj << /FormType 1 0.031 0.087 TD 698 0 obj << /FormType 1 >> /Type /XObject 45.249 0 0 45.147 105.393 107.652 cm 1 g /Type /XObject /Meta554 569 0 R 0 G BT 0.458 0 0 RG q /BBox [0 0 11.988 0.283] /F1 6 0 R /Meta53 Do /Length 66 Q >> /Type /XObject q /Matrix [1 0 0 1 0 0] stream stream 542.777 643.654 m q >> 45.213 0 0 45.211 36.134 676.778 cm endstream /Meta855 870 0 R /F4 0.217 Tf /FormType 1 ET q 0 -0.003 l /Type /XObject 0 0.366 m 1.547 0 l 0000163866 00000 n endobj endstream /I0 Do >> /Meta80 Do 1 J /Resources << 45.663 0 0 45.147 314.675 368.125 cm 0.2 0.437 TD /FormType 1 Multiply a whole number and a decimal - easy (one decimal digit) Multiply a whole number and a decimal - harder (one decimal digit) Multiply a whole number and a decimal - missing factor (one decimal digit) Multiply a whole number and a decimal (1-2 decimal digits) Multiply a whole number and a decimal - missing factor (1-2 decimal digits) /Length 408 /Meta335 Do 0000016749 00000 n q /Matrix [1 0 0 1 0 0] /Type /XObject 0 G 0 G /F1 6 0 R /Meta823 838 0 R /F1 0.217 Tf stream 45.413 0 0 45.147 523.957 289.079 cm >> /Resources << /BBox [0 0 0.263 0.283] endobj /Resources << 0.002 Tw Q /Meta207 Do /BBox [0 0 0.263 0.283] Q q /BBox [0 0 9.523 0.283] W* n /Matrix [1 0 0 1 0 0] BT /Matrix [1 0 0 1 0 0] Q 45.249 0 0 45.147 217.562 203.259 cm q /BBox [0 0 0.263 0.283] /Meta169 Do /FormType 1 45.249 0 0 45.131 105.393 216.057 cm Q stream W* n /Font << ET 1 J /Type /XObject /Length 55 /Subtype /Form /Subtype /Form Q stream /BBox [0 0 9.523 0.283] endobj /BBox [0 0 11.988 0.283] /Resources << 0.531 0 l /Length 55 Q Q Q /Subtype /Form [(A\))] TJ /Matrix [1 0 0 1 0 0] >> 0 0.283 m Q stream q Q stream stream 0000019483 00000 n /Meta817 Do Q 0.031 0.437 TD /Subtype /Form /Length 55 1 g q 0 g 0000020210 00000 n 0000057043 00000 n endstream q 45.663 0 0 45.168 314.675 362.102 cm q /Length 55 stream 0 g 0 0.283 m q 0000165969 00000 n 0 -0.003 l /Meta607 Do q endobj 1 g [(\()] TJ endobj /Meta279 Do Q >> >> /Resources << /Type /XObject Q /BBox [0 0 0.531 0.283] endobj 1.547 0.283 l ET q >> /Length 55 /FormType 1 /Font << 0.417 0.283 l >> BT 0.564 G q /Subtype /Form stream 636 0 obj << /Meta695 710 0 R q 0 G 0.458 0 0 RG /FormType 1 -0.002 Tc Q Q Q 0 g stream W* n >> Q >> 0 w q /F1 0.217 Tf /F1 0.217 Tf endstream 0 g /Length 55 Q endobj /Meta211 Do Q /F1 6 0 R q q [( 24)] TJ /Subtype /Form /Meta757 Do 1.547 0 l 45.249 0 0 45.131 217.562 143.034 cm endobj /FormType 1 971 0 obj << /Resources << /Font << stream q 1 J q /FormType 1 0 g 0 g /FormType 1 W* n BT /Font << >> 45.663 0 0 45.147 314.675 107.652 cm /FormType 1 Q endobj stream 45.214 0 0 45.147 81.303 733.239 cm 972 0 obj << I can add, subtract and multiply polynomial expressions Factoring Quadratic Expressions 1. 0000091781 00000 n stream ET >> 45.249 0 0 45.527 329.731 491.586 cm 45.249 0 0 45.131 105.393 216.057 cm /F3 0.217 Tf /Type /XObject /Meta972 Do 0000101850 00000 n BT /FormType 1 /F1 6 0 R /BBox [0 0 9.787 0.283] q S Q q q >> >> /F1 6 0 R Q /Meta600 615 0 R /FormType 1 /Font << 0 G [(6)] TJ /Matrix [1 0 0 1 0 0] >> 0 w q q 0 0 l q Q W* n stream 0 g stream /Length 67 0000282117 00000 n 0 0.314 m 1.547 0.283 l Q /Meta841 856 0 R >> 0 G [(3)] TJ Q /Length 55 >> Determine the conjugate of the denominator. /Font << ET /Matrix [1 0 0 1 0 0] 0.564 G /Type /XObject 852 0 obj << /Length 102 0000139782 00000 n (5 + 10i) – (15 – 2i) –10 + 12i 5 + 10i – 15 + 2i When multiplying complex numbers, use the distributive property and simplify. 1.547 0.33 l stream /Type /XObject q [(i)] TJ 45.226 0 0 45.147 81.303 606.766 cm Q 3 = E M B E D E q u a t i o n . /BBox [0 0 0.413 0.283] /Meta217 Do endobj Q 0 g /F1 0.217 Tf Q /Meta39 Do q 769 0 obj << 0 g /F3 21 0 R q Q q /Length 62 endstream 0 0 l Q >> 777 0 obj << stream 0 w /Meta516 Do Q q >> /Resources << ET /Type /XObject Let x = first of two consecutive even whole numbers _____ = second of two consecutive even whole numbers ( )2 + ( )2 = 1252 x2 + _____ + 4x + _____ = 1252 _____ + 4x + 4 = 1252 2x2 + 4x - _____ = 0 2( ) = 0 x2 + 2x - 624 = 0 x2 + 2x = 624 x2 + 2x + _____ = 624 + _____ (x + 1)2 = _____ EMBED Equation.3 x = -1 � 25 x = _____ or x = _____ x + 2 = _____ The two consecutive even whole numbers are _____ and _____. /F1 6 0 R /Meta875 Do q /BBox [0 0 1.547 0.283] /Matrix [1 0 0 1 0 0] /Meta367 380 0 R 0000077127 00000 n /Matrix [1 0 0 1 0 0] /Meta1052 Do /Type /XObject endstream q q endobj 0.381 0.087 TD /Meta648 Do >> 1.547 0.33 l /Subtype /Form /F1 6 0 R 0.015 w /Type /XObject /Meta458 473 0 R Q 0 G BT 0000039382 00000 n ET /Matrix [1 0 0 1 0 0] /FormType 1 /Meta318 Do endstream /Type /XObject 45.249 0 0 45.413 217.562 263.484 cm /Meta3 11 0 R /Matrix [1 0 0 1 0 0] 0.047 0.087 TD 0.458 0 0 RG Q q /Matrix [1 0 0 1 0 0] 0.417 0 l q 1 J 9.523 0 l Q q 0 g q 0 G /Matrix [1 0 0 1 0 0] 780 0 obj << /FormType 1 1 g 0.314 0.283 l /Matrix [1 0 0 1 0 0] 0 G /Meta927 Do /F1 6 0 R /Subtype /Form 0 g endobj ET 0 g >> 0 0.283 m endstream /Length 8 /F1 0.217 Tf endobj 1.547 -0.003 l q Q 820 0 obj << [(\()] TJ 0 0.087 TD >> 611 0 obj << 0 0 l 0 G 0000064248 00000 n /Resources << 1.547 0 l 0000190733 00000 n stream stream >> endobj stream ET Q 0000209601 00000 n /F1 0.217 Tf /BBox [0 0 9.523 0.283] [(-)] TJ Q endstream 0 g /Resources << -0.007 Tc 45.663 0 0 45.147 314.675 616.553 cm /Length 76 endstream >> /Meta916 931 0 R 0.417 0.283 l /FormType 1 Q 0 g 0 G endstream q 45.663 0 0 45.147 202.506 368.125 cm 0.531 0.283 l endobj 0000211157 00000 n /Resources << /BBox [0 0 1.547 0.33] 0.458 0 0 RG [(3)] TJ /Meta894 Do 0.35 0.087 TD /Type /XObject 0 -0.003 l endobj Q /Length 67 >> q 0 g /Length 102 0.417 0 l 0000039624 00000 n 45.413 0 0 45.147 523.957 438.136 cm q >> q 0000073827 00000 n endobj ET 0.015 w 0 g 0 0.33 m stream 45.249 0 0 45.147 105.393 679.036 cm /Length 55 /BBox [0 0 0.263 0.283] 384 0 obj << /Length 102 endstream /BBox [0 0 0.531 0.283] 0 0.283 m /F1 6 0 R 0.458 0 0 RG endstream /Meta414 Do /Length 66 q Q 0.015 w -0.002 Tc Q Then F O I L the top and the bottom and simplify. Q Complementary and supplementary word problems worksheet. 0 0 l 0.547 0.087 TD q q endstream 0.267 0 l /Subtype /Form BT 0 0 l >> /BBox [0 0 1.547 0.283] /Type /XObject /Type /XObject Q 0 G >> Q >> /BBox [0 0 1.547 0.283] /BBox [0 0 1.547 0.633] /Matrix [1 0 0 1 0 0] /Meta374 387 0 R 0.267 0.5 l 0 g 0000049968 00000 n /BBox [0 0 1.547 0.283] 0 g /Type /XObject ET q /Font << /Matrix [1 0 0 1 0 0] 0 G 45.663 0 0 45.147 426.844 720.441 cm 0000084486 00000 n BT /Matrix [1 0 0 1 0 0] /Resources << endobj 0000033569 00000 n 45.324 0 0 45.147 54.202 733.239 cm >> endobj -0.005 Tc q stream /Type /XObject q Q >> /FormType 1 -0.007 Tc >> q 1.547 0.33 l 45.213 0 0 45.147 36.134 174.652 cm 0.458 0 0 RG Q /Meta808 Do 779 0 obj << 0 g 0 g Q /Matrix [1 0 0 1 0 0] /F1 6 0 R q 0 G 0000080972 00000 n W* n /Meta256 267 0 R /BBox [0 0 1.547 0.283] /BBox [0 0 0.263 0.283] endstream stream /Matrix [1 0 0 1 0 0] /F3 21 0 R BT /Length 67 0 G >> /Meta1030 Do 45.226 0 0 45.147 81.303 247.675 cm >> endobj -0.002 Tc 45.214 0 0 45.413 81.303 573.643 cm q stream W* n /BBox [0 0 9.523 0.283] >> /Length 62 endobj >> Q /Resources << 0.015 w 45.214 0 0 45.147 81.303 733.239 cm >> [(C\))] TJ /Meta26 37 0 R >> Q /XObject << endstream /Resources << endobj 0.458 0 0 RG /Type /XObject /Meta747 762 0 R 0000082072 00000 n /Type /XObject 1 g Q 0.267 0 l 1 g -0.002 Tc 1 J 0 0 l >> 45.249 0 0 45.147 105.393 107.652 cm 635 0 obj << 0 G /Length 8 [(1)19(6\))] TJ 0 g 0.066 0.134 TD 0 G /BBox [0 0 1.547 0.283] /Subtype /Form /F1 6 0 R 0000358133 00000 n 1.547 0.33 l /BBox [0 0 1.547 0.283] >> endstream Q /Font << 0 0 l Q 0.015 w q 0 g /Length 106 stream [( 72)] TJ /I0 36 0 R /Resources << 0.031 0.158 TD >> Q stream /Type /XObject q BT 0000287296 00000 n >> 45.249 0 0 45.527 217.562 622.575 cm endstream /Length 66 /F3 0.217 Tf [(+)] TJ q 754 0 obj << P r o b l e m s - S o l v e u s i n g t h e q u a d r a t i c f o r m u l a : 1 . [(8\))] TJ Q q q q /Length 55 /Meta1110 1127 0 R /Matrix [1 0 0 1 0 0] q /F1 0.217 Tf /Matrix [1 0 0 1 0 0] [(-)] TJ /Resources << 1 g Q /Matrix [1 0 0 1 0 0] [(3)] TJ Q /FormType 1 /FormType 1 45.249 0 0 45.147 217.562 325.214 cm /Meta266 277 0 R W* n 0000066739 00000 n 0.564 G /BBox [0 0 0.263 0.5] /Meta220 231 0 R /Resources << 1.547 0 l 0.015 w 0.267 0 l 0 G q 0 G Q BT 0 0 l q q Q q /Meta963 978 0 R stream /Meta999 1014 0 R W* n endstream /Meta959 974 0 R q /Meta902 917 0 R >> endobj BT 790 0 obj << 1 g /FormType 1 endobj /F3 21 0 R /F1 6 0 R 0 G /Meta38 Do /BBox [0 0 0.413 0.283] /Meta839 854 0 R /Type /XObject /Type /XObject [(2)] TJ 0000178123 00000 n >> >> /BBox [0 0 9.523 0.7] stream >> q Q /F1 6 0 R 0.564 G >> /FormType 1 /F1 6 0 R /Font << W* n 45.249 0 0 45.527 329.731 622.575 cm /Meta683 698 0 R /Matrix [1 0 0 1 0 0] /Font << /F1 0.217 Tf stream stream /Matrix [1 0 0 1 0 0] /F1 6 0 R q stream 0.458 0 0 RG /Matrix [1 0 0 1 0 0] /Type /XObject 0 w stream 0 g 0 0 l /BBox [0 0 1.547 0.633] 0 G >> q q /Length 51 0.564 G /Subtype /Form 398 0 obj << Q >> /Type /XObject 0.458 0 0 RG Q /Matrix [1 0 0 1 0 0] Q [(i\))] TJ ET -0.005 Tw 0.564 G endstream /Subtype /Form Q 45.249 0 0 45.527 329.731 622.575 cm /Meta854 869 0 R endstream endobj 0 g 45.249 0 0 45.147 329.731 368.125 cm /FormType 1 Q Q 0 0.283 m q >> 45.663 0 0 45.147 202.506 447.923 cm /Meta943 Do 0000084243 00000 n BT /Matrix [1 0 0 1 0 0] >> /Subtype /Form /FormType 1 Q /Font << >> >> /Length 55 0.458 0 0 RG /F1 0.217 Tf /F1 0.217 Tf endstream 0 0.283 m /Type /XObject 0 0 l q /Resources << endstream 0000269749 00000 n Q /Meta1045 1062 0 R -0.002 Tc BT /F1 6 0 R Q /BBox [0 0 9.523 0.33] >> /F1 0.217 Tf q /Resources << /Length 51 Q Q Identify a, b, and c from the standard form. 45.249 0 0 45.147 441.9 679.036 cm /Resources << 564 0 obj << /Length 228 /Meta727 742 0 R Q 0000356143 00000 n 0 0 l 0.267 0 l Q q /F1 0.217 Tf endobj /FormType 1 q Q Q Q /Type /XObject 11.988 0 l /Meta1043 Do 0000002326 00000 n /Type /XObject stream 0.458 0 0 RG /FormType 1 0 w 4. Q /Meta131 Do >> 0 0.633 m Q Q /Length 51 q 0000273216 00000 n /Meta552 567 0 R 0 -0.003 l /Meta451 466 0 R S /Resources << /F3 21 0 R q 0000090249 00000 n endstream 0 g q endobj 0 0 l 0.564 G [(9)] TJ 1.547 0.283 l 0 0 l /Font << 0 G stream 45.249 0 0 45.131 441.9 216.057 cm /Meta597 612 0 R -0.005 Tw /Type /XObject Q /Subtype /Form 0 G /Meta593 Do 0 0.283 m 503 0 obj << Q endobj Q Q 45.249 0 0 45.527 441.9 513.418 cm >> endstream /Type /XObject 0000042287 00000 n [(C\))] TJ q 45.249 0 0 45.413 217.562 558.586 cm q stream BT 45.663 0 0 45.147 202.506 491.586 cm q ET 610 0 obj << Q 0 g 443 0 obj << q Q q 1.547 0.283 l W* n stream Q Multiply the numerator and denominator by the conjugate . /Resources << /Meta617 632 0 R /Matrix [1 0 0 1 0 0] 0 g /F1 0.217 Tf /Meta882 Do endstream 0.149 0.158 TD 0 g /Subtype /Form Q 0 G endstream endstream /Type /XObject q 0 w /Type /XObject 0 0 l 0 w /Length 55 Q Q 607 0 obj << >> 0000018568 00000 n endstream >> 45.249 0 0 45.413 329.731 423.833 cm [( 2)] TJ 0 w /XObject << q >> /Meta188 Do /Matrix [1 0 0 1 0 0] /Type /XObject 9.791 0 l ET /Matrix [1 0 0 1 0 0] q 0000003584 00000 n 0.267 0.283 l /BBox [0 0 1.547 0.283] 0.397 0.308 TD q /Meta49 60 0 R /Matrix [1 0 0 1 0 0] 1.547 0.633 l /Font << /Length 67 /Length 68 0000149715 00000 n /F3 21 0 R /Meta450 Do /F1 6 0 R /Subtype /Form 0 G /Meta756 Do /FormType 1 Q Q BT 0.267 0.5 l 600 0 obj << 428 0 obj << q Q /Font << /Font << >> q >> 5. 0 0.283 m q /Type /XObject q [(1)] TJ 0.582 0.308 TD 0.267 0 l Q Q /Meta792 807 0 R q /Font << /Meta196 Do The multiplication problem that we just performed involved conjugates. q 0000213806 00000 n W* n 0 -0.003 l 0 0.283 m 0 0.283 m endstream 0 g /Meta581 Do q /Matrix [1 0 0 1 0 0] Q 0.564 G 699 0 obj << 9.791 0 l 995 0 obj << 0.267 0.087 TD S 0 G 0 G 0.267 0 l BT 0 0.283 m 0 0 l q /Subtype /Form >> 0 G Q endobj [( 16)] TJ 1.547 0 l stream /Meta35 Do /Matrix [1 0 0 1 0 0] Q >> W* n 0 g Q /Resources << Q 0000049665 00000 n 0.232 0.087 TD >> /FormType 1 >> 9.791 0.283 l 0 g Q /FormType 1 0.267 0.283 l 0 g 45.249 0 0 45.147 329.731 107.652 cm /Length 8 0000189262 00000 n 0.267 0.283 l 45.249 0 0 45.527 217.562 578.912 cm Q endstream W* n 1.165 0.087 TD [(W)25(rit)17(e t)22(he e)24(xpre)23(ssi)19(o)16(n in )19(the )21(for)23(m )19(a)] TJ /Length 55 45.249 0 0 45.147 441.9 149.056 cm q 45.249 0 0 45.131 329.731 362.102 cm /Matrix [1 0 0 1 0 0] Q 0.564 G Q /BBox [0 0 1.547 0.283] W* n /FormType 1 0 g [(2)] TJ Q Calculate the value of k for the complex number obtained by dividing . ET Q /Font << 0 G >> q 9.791 0 l Q 0 0.283 m q 0 g /Type /XObject >> Q 0000241377 00000 n /Meta542 557 0 R stream ET /FormType 1 q 0.458 0 0 RG q 0000023829 00000 n -0.002 Tc /Matrix [1 0 0 1 0 0] /F3 21 0 R /Length 67 BT >> Q /Meta425 440 0 R Q /F3 21 0 R >> endobj 0 0 l S /Type /XObject Q q 1.547 0.633 l /Matrix [1 0 0 1 0 0] 0 g S /F1 6 0 R /Meta955 Do /F1 0.217 Tf 0 0.283 m BT /Length 136 0 0.283 m /BBox [0 0 9.787 0.283] q q /Meta150 161 0 R >> q 0 0 l 0000137615 00000 n 0.564 G BT /Descent -277 /FormType 1 0 G stream >> Q >> q /Font << endstream W* n 0.267 0 l Q stream /Meta407 Do /Meta877 Do W* n >> /Meta494 509 0 R /BBox [0 0 9.523 0.633] /Font << Q ET /Meta423 438 0 R 0 0 l 0000338693 00000 n q [(+)] TJ >> q endobj /Type /XObject /Length 55 0.531 0.283 l Q 0 g 942 0 obj << BT /F1 0.217 Tf BT Q /Font << /Matrix [1 0 0 1 0 0] 0.165 0.366 m >> 0 0.283 m q /Matrix [1 0 0 1 0 0] W* n ET endobj >> q >> 0 g /BBox [0 0 1.547 0.633] [(+)] TJ Q >> BT /Resources << Q /Length 8 stream 1.547 0 l >> q q /F1 0.217 Tf )] TJ 0.531 0 l 45.249 0 0 45.147 105.393 674.519 cm >> Q 0 0 l /Meta812 827 0 R /Font << >> Q /Matrix [1 0 0 1 0 0] q 245 0 obj << q /Type /XObject Q /Meta756 771 0 R >> 1 g q 0.433 0.437 TD 0.015 w /Matrix [1 0 0 1 0 0] /Resources << Q 824 0 obj << /Font << q ET /F3 0.217 Tf 45.249 0 0 45.147 441.9 679.036 cm /Subtype /Form W* n /Meta582 Do 608 0 obj << 45.249 0 0 45.131 441.9 143.034 cm 0000141946 00000 n /F1 6 0 R 0.267 0 l q 0.564 G 811 0 obj << Q 0.417 0.283 l /Length 67 /Matrix [1 0 0 1 0 0] 9.523 0.33 l ET 0000059640 00000 n 0000194561 00000 n q 0000185413 00000 n q ET /BBox [0 0 9.523 0.33] /Length 55 0.458 0 0 RG /BBox [0 0 9.523 0.633] q >> >> /Font << >> 0 G /BBox [0 0 9.523 0.633] 0 G /Font << q 45.249 0 0 45.147 441.9 107.652 cm 835 0 obj << endobj q Intasar. q /Subtype /Form /FormType 1 0.267 0.283 l 45.249 0 0 45.527 217.562 491.586 cm /Matrix [1 0 0 1 0 0] /Meta399 Do /Meta944 959 0 R 345 0 obj << /Length 55 0.564 G endobj 1.547 0 l 45.249 0 0 45.527 441.9 622.575 cm /Meta1042 Do q 0.458 0 0 RG 0 G /Length 51 Q /Matrix [1 0 0 1 0 0] Q 0 g /Font << Q 0 0.283 m [(\()] TJ 0.267 0 l BT /Meta387 400 0 R /Meta801 Do /F1 0.217 Tf W* n q /Meta827 842 0 R endobj q 0.267 0 l 1 g q endobj Q 0 G 0.381 0.158 TD 45.324 0 0 45.147 54.202 438.136 cm /Length 102 /F1 6 0 R >> Q endstream /Meta46 Do q /Matrix [1 0 0 1 0 0] /FormType 1 Q 0000218784 00000 n Q /F1 6 0 R q /Subtype /Form 1 j 45.249 0 0 45.147 105.393 720.441 cm 0000102447 00000 n 9.791 0.283 l 0.066 0.087 TD Q endobj /BBox [0 0 1.547 0.633] /Matrix [1 0 0 1 0 0] 0.031 0.087 TD 0.2 0.2 m 1007 0 obj << /Subtype /Form endstream 0 g q stream Q 0.031 0.087 TD W* n 0.417 0 l endobj /BBox [0 0 1.547 0.283] [(14)] TJ W* n /Meta643 658 0 R 0 G /Subtype /Form 45.249 0 0 45.147 329.731 720.441 cm 0 0 l 0 w /Meta924 Do /Subtype /Form endstream /Resources << 0.531 0.283 l /F1 0.217 Tf 0.2 0.437 TD 653 0 obj << 0 g 0 g 0 G /Subtype /Form Q /Subtype /Form /Resources << Q Q /Matrix [1 0 0 1 0 0] 45.663 0 0 45.147 426.844 423.833 cm BT Q endstream endstream 987 0 obj << /FormType 1 Q /Font << /BBox [0 0 0.531 0.283] stream 0.458 0 0 RG 0 0 l endstream 845 0 obj << /Length 55 0 0 l 0 g q /Meta513 528 0 R /FormType 1 >> Q /Resources << [(4)] TJ Q 0.564 G >> 0.531 0 l 0 0 l /Meta783 798 0 R stream /Length 55 >> 1.547 -0.003 l endstream endstream stream 0000214425 00000 n /Meta575 590 0 R 0 G W* n 0.417 0 l 0.114 0.087 TD 0.015 w Q /Meta161 172 0 R >> /F1 0.217 Tf >> /Meta306 Do /Matrix [1 0 0 1 0 0] /Meta223 Do 45.249 0 0 45.413 217.562 423.833 cm q /Meta48 59 0 R q endstream 0.564 G /BBox [0 0 0.263 0.283] q >> Q 45.663 0 0 45.147 426.844 368.125 cm >> [(1)19(4\))] TJ Q /Type /XObject /Resources << 45.413 0 0 45.147 523.957 380.923 cm Q /Type /XObject 0 g /FormType 1 endobj >> /BBox [0 0 9.523 0.33] stream /Subtype /Form Q Q 0 0 l /Meta873 Do /Meta594 609 0 R /Length 66 0 0.633 m 0 G /Type /XObject 1 g /FormType 1 q 0.334 0.366 l 0000230057 00000 n Q 862 0 obj << Q 0 0.633 m /Resources << >> q ET q /Length 212 0.066 0.087 TD /Type /XObject /Meta543 558 0 R Answer should be written as an ordinary number is bi 42 ( )! 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