# How do I find the fifth root of a complex number?

##### 1 Answer

Nov 1, 2015

Convert to polar form first, then...

#### Explanation:

A Complex number in the form

#root(5)(r)(cos (theta/5) + i sin (theta/5))#

#root(5)(r)(cos ((theta + 2pi)/5) + i sin ((theta+2pi)/5))#

#root(5)(r)(cos ((theta + 4pi)/5) + i sin ((theta+4pi)/5))#

#root(5)(r)(cos ((theta + 6pi)/5) + i sin ((theta+6pi)/5))#

#root(5)(r)(cos ((theta + 8pi)/5) + i sin ((theta+8pi)/5))#

Conventionally your original