- #1
menco
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Homework Statement
Express z=-1+4i in polar for then find z^4 converting to Cartesian form
Homework Equations
r = sqrt(x^2+y^2)
theta = y/x
z= r cos (theta) + i r sin (theta)
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)