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Find the square roots of 21 - 20*i.

 Apr 29, 2022
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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 \(5-2i\).

 Apr 29, 2022

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