Assume $j=\sqrt{-1}$, to calculate $(-3.1416j)^{0.5}$ in Matlab, I type
(j*-3.1416)^0.5 and it gives me the result: 1.2533 - 1.2533i.
However, if I calculate it in another way $(-3.1416j)^{0.5}=(-1)^{0.5}*j^{0.5}*(3.1416)^{0.5}$, i.e.,
(-1)^0.5*j^0.5*(3.1416)^0.5 and it gives me: -1.2533 + 1.2533i, which is the opposite of the first result.
Why and what's wrong here? How to solve this problem to get a consistent result? Just add a minus sign -(-1)^0.5*j^0.5*(3.1416)^0.5?
Every non-zero complex number has two square roots: if $w^2=z$, then $(-w)^2=z$ too.
You found one square root one way, and one the other. (The program gives you only one each time.)