Find the square root of $4 a b - 2 (a^{2} - b^{2}) i$ .

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Solution

Now,
$4 a b - 2 (a^{2} - b^{2}) i$
$= (a + b)^{2} - (a - b)^{2} - 2 {(a + b) (a - b)} i$
$= (a + b)^{2} + {i (a - b)}^{2} - 2 {(a + b) (a - b)} i$
$= {(a + b) - i (a - b)}^{2}$ .
So the square root of $4 a b - 2 (a^{2} - b^{2}) i$ is $\pm$ ${(a + b) - i (a - b)}$

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