$(- 3 + 2 i)^{3} = 46 i + 9$

Explanation

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$(- 3 + 2 i)^{3} \overset{◯}{1} 8 i^{3} - 36 i^{2} + 54 i - 27 \overset{◯}{2} \overset{◯}{3} - 8 i + 36 + 54 i - 27 \overset{◯}{4} 46 i + 9$
①	Find $(- 3 + 2 i)^{3}$ in two steps. S1: Swap two terms inside bracket S2: apply formula $(A - B) = A^{3} - 3 A^{2} B + 3 A B^{2} - B^{3}$ where $A = 2 i$ and $B = 3$ . $(- 3 + 2 i)^{3} S 1 (2 i - 3)^{3} = (2 i)^{3} - 3 \cdot (2 i)^{2} \cdot 3 + 3 \cdot 2 i \cdot 3^{2} - 3^{3} = 8 i^{3} - 36 i^{2} + 54 i - 27$
②	$8 i^{3} = 8 \cdot i^{2} \cdot i = 8 \cdot (- 1) \cdot i = - 8 \cdot i$
③	$- 36 i^{2} = - 36 \cdot (- 1) = 36$
④	Combine like terms: $- 8 i + 54 i + 36 - 27 = 46 i + 9$

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(−3+2i)3=46i+9

$(- 3 + 2 i)^{3} = 46 i + 9$