Question

Find the first of the nth roots of the complex number. Leave answer in polar form and use degrees for theta.

81 n=4


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I got to this part. x^4=81
theta=0,90,180, 270

Answer 1

is the complex number 81?

Answer 2

yes

Answer 3

so i must find 4 roots of 81

Answer 4

polar form of 81:
\[81(\cos 0 + i \sin0)\]
4th roots are
\[\sqrt[4]{81}(\cos \frac{0+360k}{4} + i \sin \frac{0+360k}{4})\]
where k = 0,1,2,3