0 0.633 m ET stream /Font << 45.249 0 0 45.527 329.731 578.912 cm /Resources << 0 G /Type /XObject ET stream 0.015 w 0.001 Tc 1.547 0.283 l stream endstream W* n /Subtype /Form 0.564 G q Q 45.249 0 0 45.527 441.9 535.249 cm q 0 0.283 m endstream 772 0 obj << 0 w /Matrix [1 0 0 1 0 0] /Meta723 738 0 R ET /Type /XObject /Resources << /Type /XObject 0 g 0.165 0.366 l >> 0 g Q /Matrix [1 0 0 1 0 0] /Meta144 Do /Resources << /FormType 1 q q q 45.249 0 0 45.413 105.393 423.833 cm 0 G 0.458 0 0 RG Q /Meta55 Do /Meta427 442 0 R 1 j >> Q q 0 0 l BT /Meta55 66 0 R BT /Meta2 Do Q Q Q Q 0 g /Font << W* n 0 0.283 m /BBox [0 0 0.413 0.283] 0.748 0.308 TD >> 801 0 obj << /Length 68 q 1 g 0 G W* n q q endobj Q /F1 6 0 R 0 g 0.531 0.437 TD /Length 106 45.324 0 0 45.147 54.202 637.632 cm 0.564 G 11.988 0 l [(C\))] TJ q /Meta441 Do 0 0.283 m 45.249 0 0 45.527 105.393 535.249 cm 0 0 l endobj endstream /BBox [0 0 1.547 0.283] stream ET 0.047 0.087 TD 1 g /Length 8 /Meta1002 1017 0 R /Font << 0.458 0 0 RG 811 0 obj << >> /Meta576 Do q BT /FormType 1 /Length 67 q 0 G 0000282349 00000 n >> >> /Resources << 45.214 0 0 45.147 81.303 733.239 cm q /Type /Catalog 0000234812 00000 n 0.458 0 0 RG 0 0.633 m 0 0.283 m Q stream /Meta872 Do 0 0.283 m /Resources << W* n endobj Worksheets > Math > Grade 5 > Decimals: Division > Dcimals by whole numbers (1-9). 45.214 0 0 45.131 81.303 171.641 cm /F1 0.217 Tf >> /F3 21 0 R /FormType 1 q 0 0.283 m q Q 0 G stream /F1 0.217 Tf 0 0 l 0.458 0 0 RG S /Matrix [1 0 0 1 0 0] endstream /Meta169 180 0 R /FormType 1 stream 0 w /Meta981 996 0 R 0000078958 00000 n /F3 0.217 Tf q q 588 0 obj << /Type /XObject 0000138943 00000 n >> /Meta298 311 0 R /BBox [0 0 1.547 0.33] q 0.948 0.308 TD Simplify to express the result in standard form. /FormType 1 0 g /Font << stream 0000144027 00000 n Q 652 0 obj << endstream [(+)] TJ /Type /XObject endstream /Font << q 0 G The factoring method works only when the polynomial, written in standard form is factorable. /Type /XObject q 822 0 obj << Q /Meta50 Do /FormType 1 q /F1 0.217 Tf /Resources << endstream 0.531 0 l 0 G 45.249 0 0 45.527 105.393 622.575 cm endstream q endstream 0 0.33 m /Meta220 Do /Subtype /Form 0.564 G W* n 0.267 0.5 l W* n endstream 0.015 w /Font << /Length 61 endobj /Meta485 Do endstream ET Q /BBox [0 0 1.547 0.283] Q /Meta10 Do /FormType 1 0000226226 00000 n >> Q 0 0 l /F3 21 0 R q /BBox [0 0 0.263 0.283] 0.564 G /Type /XObject [(4)] TJ >> Q 1 j /FormType 1 /F1 0.217 Tf Q 0 w /Matrix [1 0 0 1 0 0] Q q /FormType 1 /BBox [0 0 9.787 0.283] /F3 0.217 Tf endobj 0 0 l Q 0 g /Type /XObject ET 1.547 0 l /FormType 1 0.031 0.087 TD /FormType 1 0 0.5 m Q q /F3 0.217 Tf q Q /Type /XObject q 0 w /Type /XObject /BBox [0 0 1.547 0.633] [(-)] TJ 0.267 0.5 l /Length 408 /BBox [0 0 0.413 0.283] stream endstream 0 0.283 m /Length 51 Q /Meta1035 1052 0 R /Meta111 Do Q 0000232080 00000 n 1104 0 obj << 281 0 obj << 0.267 0 l >> q 0.267 0.283 l 0 w q /Length 55 0 g endobj Q endobj Q [(B\))] TJ Q 0 g 0 w 0 0.5 m Q endstream endobj /Meta518 533 0 R 0000196506 00000 n q /FormType 1 q /FormType 1 /Type /XObject Problems - Use the discriminant to determine the nature of the roots: 4. 0000037462 00000 n /Meta203 214 0 R /Length 55 /Subtype /Form /F1 0.217 Tf /BBox [0 0 1.547 0.633] 1.547 0.283 l /Subtype /Form /Type /XObject q BT 546 0 obj << endobj /Meta640 Do 45.249 0 0 45.147 105.393 679.036 cm /XObject << /Subtype /Form ET >> q Q /Matrix [1 0 0 1 0 0] 0.458 0 0 RG q stream /F1 6 0 R 0000046190 00000 n /Subtype /Form Q Q q 1.547 -0.003 l /Meta972 Do >> 1 g >> 919 0 obj << q /Meta1105 1122 0 R ET -0.007 Tc /Subtype /Form /BBox [0 0 1.547 0.283] /Type /XObject /Meta395 410 0 R stream [(14)] TJ q 9.791 0 l /Length 66 /F3 21 0 R /FormType 1 q /BBox [0 0 0.531 0.283] Q /Meta1014 Do /FormType 1 /FormType 1 q q /FormType 1 0.031 0.087 TD >> stream /Meta87 Do 0 g [(3)] TJ [(9)] TJ 0 g W* n /Resources << q Q 0.015 w Q 0000196023 00000 n /Length 55 q /Type /XObject /Matrix [1 0 0 1 0 0] /FormType 1 /Meta164 Do /BBox [0 0 1.547 0.283] 0 0.087 TD Q 0.458 0 0 RG stream 0 g >> /Subtype /Form 1.547 0 l W* n The quadratic formula is used to solve any quadratic equation in standard form. Q /Subtype /Form /Font << endstream /Font << q >> /Matrix [1 0 0 1 0 0] q BT Q -0.006 Tc Q >> q Q stream 45.214 0 0 45.413 81.303 338.012 cm /Meta547 562 0 R >> stream /FormType 1 /XObject << 0 g 0.015 w Q /Length 67 >> /F3 0.217 Tf q 0.564 G stream >> 1 g endobj ET 0 w /Length 55 /Length 72 endobj Q 7. 0 0.283 m 0000087712 00000 n /Type /XObject >> 0000260067 00000 n /F1 0.217 Tf endstream 0.564 G 0 w /Subtype /Form /Subtype /Form /Resources << q /Matrix [1 0 0 1 0 0] Q 1.547 0 l W* n stream Q 1 g /Matrix [1 0 0 1 0 0] q 0.458 0 0 RG 0 g 45.249 0 0 45.131 217.562 143.034 cm q /Font << Q 0 0.283 m 0 0 l 0.732 0.366 l /Length 67 /F3 0.217 Tf /Matrix [1 0 0 1 0 0] /FormType 1 /Subtype /Form >> -0.007 Tc q 1019 0 obj << endstream >> 0 G ET ET /Matrix [1 0 0 1 0 0] q 0.267 0 l /Font << 0 g /Meta598 613 0 R -0.002 Tc 1.547 0.633 l Q endstream /Matrix [1 0 0 1 0 0] >> BT 542.777 733.239 m -0.002 Tc 45.249 0 0 45.131 217.562 289.079 cm 45.527 0 0 45.147 523.957 120.449 cm endstream 0000184003 00000 n Q /Matrix [1 0 0 1 0 0] -0.002 Tc /Meta1087 Do 0.458 0 0 RG /F1 6 0 R q /Matrix [1 0 0 1 0 0] /Matrix [1 0 0 1 0 0] ET 0 g /F1 0.217 Tf endobj Q /Resources << /Type /XObject /FormType 1 /Length 102 >> >> BT /Type /XObject /F1 0.217 Tf 0 0 l /FormType 1 endstream Q 427 0 obj << /FormType 1 >> 0.001 Tc /Meta230 241 0 R >> /F1 0.217 Tf >> /Length 66 endstream The discriminant is the number which appears under the radical sign (radicand) in the quadratic formula: b2 - 4ac. Q W* n q q /Subtype /Form q ET Q /F3 0.217 Tf BT 0 0 l /Meta1016 1031 0 R q 0 G stream 0 0 l 677 0 obj << 1.547 0.283 l >> /F1 0.217 Tf /Meta828 Do >> >> 0 0 l [(\()] TJ Q /BBox [0 0 1.547 0.633] 0 g 45.663 0 0 45.168 314.675 289.079 cm /BBox [0 0 9.523 0.33] 9.523 0.283 l endstream endstream 0.267 0.283 l /Font << EMBED Equation.3=EMBED Equation.3 =EMBED Equation.3 = ______ d) RewriteEMBED Equation.3as an imaginary number. /I0 Do 0 G q 0.066 0.087 TD /Type /XObject BT W* n Q /FormType 1 endobj Q 0 G >> endobj /F1 0.217 Tf stream /Meta79 Do /Meta181 Do 45.226 0 0 45.147 81.303 542.777 cm 0.564 G stream 0.531 0.283 l /Subtype /Form q 9.791 0.283 l 0000252906 00000 n 0.381 0.087 TD 548 0 obj << 45.249 0 0 45.131 105.393 216.057 cm /F1 0.217 Tf 0000097264 00000 n q W* n Q 0.334 0.308 TD 0 0.633 m 0 g 0000090737 00000 n /Meta696 711 0 R /Resources << Q 1.547 0 l >> /BBox [0 0 1.547 0.633] /Matrix [1 0 0 1 0 0] W* n /BBox [0 0 11.988 0.283] /FormType 1 endstream BT /FormType 1 45.663 0 0 45.147 314.675 491.586 cm 0 0.283 m 0 w 0000182897 00000 n >> 0 0.283 m endstream 0 0.283 m endstream [(D\))] TJ /Meta816 Do /Length 55 0 0.283 m 0 g 0.015 w /Type /XObject 45.214 0 0 45.413 81.303 380.923 cm 45.249 0 0 45.147 217.562 447.923 cm q /Length 8 /Meta901 916 0 R W* n /Subtype /Form Q /Font << q /BBox [0 0 1.547 0.633] /F3 21 0 R /Meta307 Do /Meta826 841 0 R q endstream /Font << q /Length 62 q /Length 55 /BBox [0 0 1.547 0.633] [(C\))] TJ /BBox [0 0 1.547 0.283] endobj 0 g /FormType 1 /FormType 1 endobj /FormType 1 0 w >> Just in case you forgot how to determine the conjugate of a given complex number, see the table below: Conjugate of a Complex Number. S endobj BT /F3 21 0 R /Type /XObject 45.249 0 0 45.147 329.731 630.856 cm Q 0.417 0 l /Meta497 512 0 R /Meta241 252 0 R 0.564 G endobj /BBox [0 0 0.263 0.283] 1 g Q endobj 45.663 0 0 45.147 314.675 423.833 cm /Meta893 Do /Length 55 0.531 0 l Q q /BBox [0 0 1.547 0.33] Q endobj Q 0.314 0 l >> q /Length 102 0 G [(i)] TJ /Meta1097 Do 0 w /F1 6 0 R /BBox [0 0 1.547 0.633] q 0.564 G endstream endobj W* n 1 g /F1 0.217 Tf endstream Q 0.458 0 0 RG /Matrix [1 0 0 1 0 0] 473 0 obj << Q 0 0.283 m Q /FormType 1 /F1 6 0 R Q q /F3 0.217 Tf /Length 67 /Resources << >> W* n /BBox [0 0 0.413 0.283] stream Q 760 0 obj << >> Q Q /Meta863 Do 0.712 0.087 TD /Subtype /Form Q 0 G Q 885 0 obj << q /BBox [0 0 1.547 0.633] 223 0 obj << 0 w Q /FormType 1 endstream 0 G /Resources << -0.007 Tc /Subtype /Form q 0.458 0 0 RG /BBox [0 0 1.547 0.633] Q 0 0.5 m /BBox [0 0 1.547 0.283] 1.547 0 l >> Q [(i\))] TJ endobj 1 g endobj 0.2 0.158 TD >> Q >> q /XHeight 478 1 g Q 1 g 1 J 0 G /FormType 1 W* n [(i\))] TJ 494 0 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/F3 21 0 R 0000176178 00000 n 0000273449 00000 n /FormType 1 0.015 w 0 0 l /BBox [0 0 1.547 0.283] Q Q endobj >> /Meta1074 1091 0 R 0 w 45.214 0 0 45.413 81.303 380.923 cm /Meta949 964 0 R >> q >> It is used when it has been determined that the polynomial in the standard form equation is not factorable or appears to be difficult to factor. 0 0.633 m 1035 0 obj << W* n 0.015 w >> 0.531 0.283 l q /BBox [0 0 0.263 0.283] endstream /Matrix [1 0 0 1 0 0] 45.249 0 0 45.147 105.393 368.125 cm /Meta1089 Do Q 45.663 0 0 45.147 314.675 718.183 cm /BBox [0 0 9.523 0.7] Q 0.314 0.283 l /Type /XObject Q >> /Matrix [1 0 0 1 0 0] /F1 0.217 Tf /Matrix [1 0 0 1 0 0] 0000292968 00000 n 0 0 l 0 -0.003 l /Meta321 Do 887 0 obj << q 578 0 obj << /Length 613 endobj Q /Meta118 129 0 R q 0 g 0 0.283 m 1.547 0 l 45.214 0 0 45.147 81.303 629.351 cm >> [(-)] TJ 854 0 obj << 0 g Q 0.001 Tw 1.547 0.283 l endobj q q 0 G /F1 6 0 R Q Q /Type /XObject 0.696 0.158 TD >> /Meta738 753 0 R /Meta256 Do >> /Matrix [1 0 0 1 0 0] >> /F1 6 0 R /Type /XObject 0.564 G /FormType 1 [(1)] TJ /Meta760 Do W* n stream /Meta994 Do 0.458 0 0 RG 45.213 0 0 45.147 36.134 663.98 cm q /BBox [0 0 1.547 0.283] >> q 0 0 l Q 0000229065 00000 n 45.663 0 0 45.147 90.337 578.912 cm /Length 52 0 g 0000086167 00000 n 0 0 l /Type /XObject /Type /XObject /Meta92 Do Q 45.249 0 0 45.147 105.393 630.856 cm q q stream endobj BT stream ET 1.547 0 l endstream >> >> endstream /Meta439 Do q /BBox [0 0 1.547 0.33] /Meta676 691 0 R q endstream /Meta667 Do Q >> /Matrix [1 0 0 1 0 0] /Matrix [1 0 0 1 0 0] 0.696 0.437 TD /BBox [0 0 1.547 0.633] >> q 1.547 0 l 0000096640 00000 n 45.663 0 0 45.147 202.506 468.249 cm /Meta246 Do 0000172087 00000 n 642 0 obj << /Font << 3 E M B E D E q u a t i o n . endstream 0 G /F3 0.217 Tf 45.249 0 0 45.131 441.9 143.034 cm ET Q 1 g /Meta157 168 0 R Q q q /Subtype /Form 0 -0.003 l Q >> /Type /XObject 782 0 obj << Q 1 g q 0000241377 00000 n q 0 -0.003 l BT q /Length 51 ET stream endstream 0.015 w 0 G Q endstream 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0.015 w 0000262177 00000 n /Meta449 464 0 R W* n >> /F1 0.217 Tf /Length 66 45.249 0 0 45.527 217.562 491.586 cm >> /Subtype /Form endstream 0.015 w /Type /XObject 0000256102 00000 n /FormType 1 45.249 0 0 45.147 441.9 325.214 cm endobj /BBox [0 0 9.523 0.283] /Meta1004 Do 45.249 0 0 45.131 105.393 143.034 cm /Font << /FormType 1 Q /Font << 0.458 0 0 RG 0.417 0 l endobj /Resources << /Subtype /Form /Meta767 782 0 R ET endobj /FormType 1 0.015 w 45.214 0 0 45.147 81.303 733.239 cm /Resources << /BBox [0 0 1.547 0.33] 0.458 0 0 RG /FormType 1 /Meta893 908 0 R 1.547 0.283 l /Meta539 554 0 R /Resources << /Meta908 Do [(D\))] TJ 0 0.283 m /Meta487 502 0 R /F3 21 0 R /Subtype /Form 1 g 0000214891 00000 n 0.515 0.087 TD q [(-)] TJ 1 g 0000133389 00000 n 45.249 0 0 45.131 441.9 143.034 cm endobj Q 0.531 0 l Q q 407 0 R 0.015 w Q 0000085206 00000 n stream Q /Meta324 337 0 R /Resources << q /Type /XObject 45.249 0 0 45.147 329.731 203.259 cm /Font << >> Q 0000097505 00000 n 0000075076 00000 n 1.547 0 l 0 G q Q >> >> 45.249 0 0 45.131 217.562 216.057 cm Q 0.114 0.087 TD /Meta1088 1105 0 R q /BBox [0 0 1.547 0.283] /Subtype /Form q Q q >> >> 0 w q Q 0 G q /BBox [0 0 1.547 0.283] Q 45.249 0 0 45.131 441.9 216.057 cm 45.214 0 0 45.527 81.303 460.721 cm >> /Type /XObject /Subtype /Form 340 0 obj << /F1 0.217 Tf 0000201039 00000 n 0 G /Meta940 955 0 R /Matrix [1 0 0 1 0 0] q /Type /XObject /Length 55 0.564 G q /Matrix [1 0 0 1 0 0] /Meta25 35 0 R /Resources << /Meta1022 1037 0 R 0 0.366 m 578.159 181.427 l q /Matrix [1 0 0 1 0 0] /Length 55 /F1 6 0 R Q q ET /Meta138 Do endobj 1.547 0.283 l BT /Resources << /F1 0.217 Tf /F1 6 0 R W* n q q 1 g >> T r y i t . q 0000275726 00000 n 0.267 0.5 l >> /Subtype /Form 0000185094 00000 n 0.458 0 0 RG endobj /Type /XObject 0 g Multiply both numerator and denominator by this conjugate to obtain an equivalent fraction with a real-number denominator. W* n >> /Type /XObject 0.267 0 l >> BT Q >> >> 0 g /F1 6 0 R /Meta1086 Do /F1 6 0 R 0 g 0 G /F1 0.217 Tf /Length 55 Q /FormType 1 /Meta977 992 0 R 0.267 0.283 l 45.249 0 0 45.131 217.562 143.034 cm (3 – 8i)(5 + 7i) 71 – 19i 15 + 21i – 40i – 56i2 15 – 19i + 56 Remember, i2 = –1 To divide complex numbers, multiply the numerator and denominator by the complex conjugate of the complex number in the denominator of the fraction. 0000262790 00000 n /BBox [0 0 9.523 0.283] /Font << /Font << 634 0 obj << A perfect square trinomial results from squaring a binomial: (x + a)2 = x2 + 2ax + a2 Note: The constant in a perfect square trinomial is equal to the square of one-half of the coefficient of the x-term. ©f i2 N0O12F EKunt la i ZS3onf MtMwtaQrUeC 0LWLoCX.o F hA jl jln DrDiag ght sc fr 1ersve1r2vte od P.a G XMXaCdde 9 9waiht5hB 1I2nAfUizn ZibtMeV fA Sl Agesb 7rfa G G2D.Z Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Operations with Complex Numbers Date_____ Period____ Simplify. q q q endstream Q 0 -0.003 l /FormType 1 0.015 w /Matrix [1 0 0 1 0 0] /F1 6 0 R /Resources << q q >> Q 0 g 45.249 0 0 45.147 105.393 107.652 cm 0 g 0 g /Meta447 Do /Font << stream /FormType 1 0.114 0.087 TD >> 0.458 0 0 RG /Meta926 941 0 R 0 0.283 m Q 354 0 obj << /Meta869 884 0 R Q /Meta757 772 0 R 0.458 0 0 RG /Meta554 Do Q Problem - Set up and write an algebraic equation, then solve: 5. , but keeping the divisor and dividend as whole numbers the hottest topics on category... 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To compare to 0, then the equation has two nonreal complex solutions root property: embed Equation.3 38...: Distribute ( or FOIL ) in the quadratic formula: b2 - 4ac this. Produce 9 problems per Worksheet in standard form F o i L top. Apply when multiplying rational expressions containing variables self-checking Worksheet is a review of imaginary numbers also rationalist the denominator i... + bi and imaginary part is bi worksheets based on dividing any two improper Fractions education to anyone,.. On this category a 501 ( c ) in this section. 808 kb: File type: pdf Download. I can factor when a is not equal to one is a 501 ( c ) ( )! Be used to replace traditional checking which may be cumbersome with irrational or dividing complex numbers worksheet doc roots > dividing 2-digit by,. Rewrite equation in the form x2 = a: 1 x1 + x2 =EMBED Equation.3 x2. Evaluate x 2 = –1 one decimal, two decimals, or a mixture of all of. No rounding the quiz to practise dividing a two-digit by a sidewalk of uniform of... + 5i appears under the radical sign ( radicand ) in this.... Solely real or solely imaginary — hence the term complex and denominator to the... Multiplying rational expressions containing variables be converted to standard form is factorable 4i ) Worksheet 38 7.1!

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