Complex numbers

Let a, b be real numbers and suppose $(a + bi)^2 = 21-20i\\$.

$a^2 - b^2 + 2abi = 21-20i\\ \begin{cases}a^2 - b^2 = 21\\2ab = -20\end{cases}$

Solving this system, $\begin{cases}a = 5\\b = -2\end{cases}$ or $\begin{cases}a = -5\\b = 2\end{cases}$.

The square roots are $-5+2i$ and $5-2i$.