$2 (2 - 3 i)^{2} + 2 - 3 i - 3 = - 27 i - 11$

Explanation

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$2 (2 - 3 i)^{2} + 2 - 3 i - 3 \overset{◯}{1} 2 (4 - 12 i + 9 i^{2}) + 2 - 3 i - 3 \overset{◯}{2} 2 (4 - 12 i - 9) + 2 - 3 i - 3 \overset{◯}{3} 2 (- 12 i - 5) + 2 - 3 i - 3 \overset{◯}{4} - 24 i - 10 + 2 - 3 i - 3 \overset{◯}{5} - 27 i - 8 - 3 \overset{◯}{6} - 27 i - 11$
①	Find $(2 - 3 i)^{2}$ using formula. $(A - B)^{2} = A^{2} - 2 \cdot A \cdot B + B^{2}$ where $A = 2$ and $B = 3 i$ . $(2 - 3 i)^{2} = 2^{2} - 2 \cdot 2 \cdot 3 i + (3 i)^{2} = 4 - 12 i + 9 i^{2}$
②	$9 i^{2} = 9 \cdot (- 1) = - 9$
③	Combine like terms: $4 - 12 i - 9 = - 12 i - 5$
④	Multiply $2$ by $(- 12 i - 5)$ $2 \cdot (- 12 i - 5) = - 24 i - 10$
⑤	Combine like terms: $- 24 i - 10 + 2 - 3 i = - 27 i - 8$
⑥	Combine like terms: $- 27 i - 8 - 3 = - 27 i - 11$

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2(2−3i)2+2−3i−3=−27i−11

$2 (2 - 3 i)^{2} + 2 - 3 i - 3 = - 27 i - 11$