$(- 5 + 10 i)^{2} = - 100 i - 75$

Explanation

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$(- 5 + 10 i)^{2} \overset{◯}{1} 25 - 100 i + 100 i^{2} \overset{◯}{2} 25 - 100 i - 100 \overset{◯}{3} - 100 i - 75$
①	Find $(- 5 + 10 i)^{2}$ in two steps. S1: Change all signs inside bracket. S2: Apply formula $(A - B)^{2} = A^{2} - 2 \cdot A \cdot B + B^{2}$ where $A = 5$ and $B = 10 i$ . $(- 5 + 10 i)^{2} S 1 (5 - 10 i)^{2} S 2 5^{2} - 2 \cdot 5 \cdot 10 i + (10 i)^{2} = = 25 - 100 i + 100 i^{2}$
②	$100 i^{2} = 100 \cdot (- 1) = - 100$
③	Combine like terms: $- 100 i + 25 - 100 = - 100 i - 75$

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(−5+10i)2=−100i−75

$(- 5 + 10 i)^{2} = - 100 i - 75$