# How do you find the square root of 8i?

##### 2 Answers

Mar 25, 2018

#### Explanation:

Mar 25, 2018

#### Explanation:

Note that:

#8i = 8(cos (pi/2) + i sin (pi/2))#

Hence by de Moivre's theorem, one square root is:

#sqrt(8)(cos(pi/4)+isin(pi/4)) = 2sqrt(2)(1/sqrt(2)+1/sqrt(2)i) = 2+2i#

This is the principal square root. The other square root is