- #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?