$\frac{4 - 2 i}{2 i ( i - 1 ) ^{2}} = \frac{4 - 2 i}{4}$

Explanation

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$\frac{4 - 2 i}{2 i ( i - 1 ) ^{2}} \overset{◯}{1} \frac{4 - 2 i}{2 i ( 1 i ^{2} - 2 i + 1 )} \overset{◯}{2} \frac{4 - 2 i}{2 i ( - 1 - 2 i + 1 )} \overset{◯}{3} \frac{4 - 2 i}{2 i \cdot - 2 i} \frac{4 - 2 i}{- 4 i ^{2}} \overset{◯}{4} \frac{4 - 2 i}{4}$
①	Find $(i - 1)^{2}$ using formula. $(A - B)^{2} = A^{2} - 2 \cdot A \cdot B + B^{2}$ where $A = i$ and $B = 1$ . $(i - 1)^{2} = i^{2} - 2 \cdot i \cdot 1 + 1^{2} = i^{2} - 2 i + 1$
②	$i^{2} = - 1$
③	Combine like terms: $- 1 - 2 i + 1 = - 2 i$
④	$- 4 i^{2} = - 4 \cdot (- 1) = 4$

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$\frac{4 - 2 i}{2 i ( i - 1 ) ^{2}} = \frac{4 - 2 i}{4}$