- #1

314Jason

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## Homework Statement

Use de Movire to find solutions for the following:

z^5 = i

z^4 = i

z^3 = i

Find generalization for z^n = x+iy,

where modulus of x+iy is 1

Explore when |x+iy| is not equal to 1

## Homework Equations

[rcis(theta)] = (r^n)cis(theta*n)

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

theta = arctan(y/x)

Finding the roots of complex numbers: (r^1/n)cis(2kpi/n), where k = 0,1,...n-1

## The Attempt at a Solution

I tried using moivre's theorem to find the roots of z, but I ended up with theta=arctan(1/0), so it is undefined. Yes, and now I'm stuck. Could the answer possibly be undefined/no solution?