Apply deMoivre formula. The square root of -10i has two different values.

Their modulus is .  Their arguments are    and  = .


So, one value of the square root is   =  = .


The other value of the square root is   =  = .


ANSWER.  Two values of the square root of -10i are    and  .

Ikleyn should have simplified

 

 

 

 

 

And similarly, the other solution is

 

Edwin

Here's another way to do this problem:

Assume

, where a and b are real numbers.







Set real parts on the left and right equal, and same with imaginary parts:







ab=-5 tells us that a and b have opposite signs, thus a=-b


 and 
or
 and 

Thus the answers are

 and 

Edwin