# How do you convert #sqrt(3+4i) # to polar form?

##### 2 Answers

#### Explanation:

Only for real

So, the other square root

Here, for sqrt(z), where z is complex, we cannot conveniently take

one and keep off the other.

So,

They are

where

using De Moivre's theorem

using

#### Explanation:

Note that:

#(2+i)^2 = 4+4i+i^2 = 3+4i#

Since

Further note that:

#abs(2+i) = sqrt(2^2+1^2) = sqrt(5)#

So we have:

#sqrt(3+4i) = 2+i = (sqrt(5), tan^(-1)(1/2))#