(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Express z=-1+4i in polar for then find z^4 converting to Cartesian form

2. Relevant equations

r = sqrt(x^2+y^2)

theta = y/x

z= r cos (theta) + i r sin (theta)

3. The attempt at a solution

r= sqrt(-1^2+4^2)

= sqrt(17)

theta = tan a = 4/1

a = tan^-1 (4/1)

= 1.3258

pi-a = 1.8158 (to find the argument from the real axis)

in polar form = sqrt(17) cis 1.8158

Then to cartesian form

z^4 = r^4 cos 4(theta) + i r^4 sin 4(theta)

= (sqrt (17))^4 cos 4(1.8158) + i (sqrt(17))^4 sin 4(1.8158)

= 289 cos 7.2632 + i 289 sin 7.2632

z = 4sqrt(160.9760) + 4sqrt(240.0161) i

z = 3.5620 + 3.9360 i

Im not sure if this is correct but hopefully i am on the right track. I was not sure if I was converting to Cartesian form correctly or if i should introduce z^4 at the polar form so that z^4 = r^4 cis 4(theta)

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# Homework Help: Complex Numbers

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