what are the roots of square root of 1-1.73j giving results in the rectangular and in exponential form
Is that really 1.73 or is it ? I am going to assume you mean .
Once you have in polar form, , which is what Twig gave you, its square roots are and .
Here, is the "principle" root of the real number r: for this problem and . (Twig's value was but I prefer . They give the same z.)
So the square roots of are and .
(Sorry, but I just can't bring myself to write "j" instead of "i"! Oh, those engineers and their jmaginary numbers!)