Solving the square roots of a complex number

Tuesday, 24 April 2018

3:35 PM

If we're asked to

 

In other words,

 

We cannot convert  into Polar form easily

 

Instead, recall the identity of a complex number in Cartesian Form

 

Therefore

 

Here we can equate the real and imaginary parts

 

 

We can then equate these two equations, and apply the quadratic formula to get

However,  as ! (From , both  and  are real numbers)

Therefore , and . So

 

Therefore