# DeMoivre’s Theorem states, “If z = r(cos u + i sin u), then zn = rn(cos nu + i sin nu). Verify for n=2?

Update:

Ok, the z^2 instead of z2 is really confusing me. Can someone explain why it becomes squared instead of doubled?

Relevance

DeMoivre's Theorem allows you to find powers of complex numbers. Given the complex number

z = r(cos u + i sin u)

Square both sides,

z² = r²(cos² u + 2icos u sin u + i²sin² u)

= r²(cos² u + 2icos u sin u - sin² u)

= r²[(cos² u - sin² u) + i(2 sin u cos u)]

= r²(cos 2u + i sin 2u)

So it's true for n = 2.