We can multiply and divide cis form of complex numbers easily and quickly. To mu

Question

We can multiply and divide cis form of complex numbers easily and quickly. To multiply two complex numbers in cis form, multiply the r's and add the angles. If v = 2 cis 120 degree and w = 5 cis 80 degree, then v * w = 10 cis 200 degree. To divide two complex numbers you the r's and the angles. an also raise complex numbers to powers or roots (exponents). To solve a complex number raised to a power, we 'r' to the power (exponent) and multiply the angle by the power. Remember to keep the angle within [0 degree, 360 degree) 5 cis 80 degree, then w^2 = 52 cis 2 * 80 degree = 25 cis 160 degree. lf u = 4 cis 80 degree and w = 2 cis 110 degree, find u * w, u/w, u^3. Show your work.

Explanation / Answer

Tow divide comlex numbers in cis form we must divide the r's of two numbers and subtract the angles

u = 4cis80 ; w = 2cis110

u*w = 4*2cis(190)

u/w = (4/2)cis(80 -110) = 2cis(-30)

u^3 = (4cis80)^3 = 4^3cis(240) = 64cis(240)

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