$(3 - 7 i) \cdot (7 + 8 i) + 7 + 6 i - 8 + 2 i = - 17 i + 76$

Explanation

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$(3 - 7 i) \cdot (7 + 8 i) + 7 + 6 i - 8 + 2 i \overset{◯}{1} 21 + 24 i - 49 i - 56 i^{2} + 7 + 6 i - 8 + 2 i \overset{◯}{2} - 56 i^{2} - 25 i + 21 + 7 + 6 i - 8 + 2 i \overset{◯}{3} 56 - 25 i + 21 + 7 + 6 i - 8 + 2 i \overset{◯}{4} - 25 i + 77 + 7 + 6 i - 8 + 2 i \overset{◯}{5} - 19 i + 84 - 8 + 2 i \overset{◯}{6} - 17 i + 76$
①	Multiply each term of $(3 - 7 i)$ by each term in $(7 + 8 i)$ . $(3 - 7 i) \cdot (7 + 8 i) = 21 + 24 i - 49 i - 56 i^{2}$
②	Combine like terms: $21 + 24 i - 49 i - 56 i^{2} = - 56 i^{2} - 25 i + 21$
③	$- 56 i^{2} = - 56 \cdot (- 1) = 56$
④	Combine like terms: $56 - 25 i + 21 = - 25 i + 77$
⑤	Combine like terms: $- 25 i + 77 + 7 + 6 i = - 19 i + 84$
⑥	Combine like terms: $- 19 i + 84 - 8 + 2 i = - 17 i + 76$

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(3−7i)⋅(7+8i)+7+6i−8+2i=−17i+76

$(3 - 7 i) \cdot (7 + 8 i) + 7 + 6 i - 8 + 2 i = - 17 i + 76$