Evaluate Complex Numbers: \sqrt{\frac{1+j}{4-8j}}

[GreenPrint]

Homework Statement

Evaluate (find the real and complex components) of the following numbers, in either rectangular or polar form:

$\sqrt{\frac{1+j}{4-8j}}$

Homework Equations

The Attempt at a Solution

I get to here and am not sure where to go from here

$\sqrt{-1/20+3/20j}$

I noticed that I can't used euler's identity here because (-1/20)^2+(3/20)^2 is not one. Thanks for any help you can provide

 

[Dick]

This would be a good time to change -1/20+3j/20 to polar form.

 

[jbunniii]

I noticed that I can't used euler's identity here because (-1/20)^2+(3/20)^2 is not one.

Can you factor out a real number from $-1/20 + 3i/20$ so that what remains has unit magnitude? i.e. write it in the form

$$\frac{-1}{20} + \frac{3i}{20} = r(a + ib)$$

where $a^2 + b^2 = 1$