1. The problem statement, all variables and given/known data I'm beginning my studies in complex variables and have some questions... Q1) We know that x2=9 => x=+/- √9 = +/- 3. Suppose z^2 = w where z and w are COMPLEX numbers, then is it still true to say that z = +/- √w ? Why or why not? Q2) "Let az2 + bz + c =0, where a,b,c are COMPLEX numbers, a≠0. Then the usual quadratic formula still holds." My concern is with the √(b2-4ac) part. How can we find √(b2-4ac) when b2-4ac is a COMPLEX number? For example, what does √(-1+4i) mean on its own and how can we find it? I know there is a general procedure(using polar form and angles) to solve for the nth root of a complex number (z^n=w), but I still don't understand what √(-1+4i) means on its own. Even for real numbers, there is a difference between solving x2=9 and finding √9, right? So is there any difference between finding √(-1+4i) and solving z2=-1+4i for z using polar form and angles? 2. Relevant equations Complex variables 3. The attempt at a solution As shown above. I hope someone can explain these. Any help is much appreciated!