How do you use De Moivre’s Theorem to find the powers of complex numbers in polar form?

Question

6486 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-12-03T02:36:55

If the complex number #z# is

#z=r(cos theta + i sin theta)#,

then #z^n# can be written as

#z^n=[r(cos theta+i sin theta)]^n=r^n[cos theta+i sin theta]^n#

by De Mivre's Theorem,

#=r^n[cos(n theta)+i sin(n theta)]#

I hope that this was helpful.