$(1 + i) \cdot (3 - i) - (3 + i) \cdot (1 - i) = 4 i$

Explanation

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$(1 + i) \cdot (3 - i) - (3 + i) \cdot (1 - i) \overset{◯}{1} 3 - i + 3 i - i^{2} - (3 - 3 i + i - i^{2}) \overset{◯}{2} - i^{2} + 2 i + 3 - (- i^{2} - 2 i + 3) \overset{◯}{3} 1 + 2 i + 3 - (1 - 2 i + 3) \overset{◯}{4} 2 i + 4 - (- 2 i + 4) \overset{◯}{5} 2 i + 4 + 2 i - 4 2 i + 4 + 2 i - 4 \overset{◯}{6} 4 i$
①	Multiply each term of $(1 + i)$ by each term in $(3 - i)$ . $(1 + i) \cdot (3 - i) = 3 - i + 3 i - i^{2}$ Multiply each term of $(3 + i)$ by each term in $(1 - i)$ . $(3 + i) \cdot (1 - i) = 3 - 3 i + i - i^{2}$
②	Combine like terms: $3 - i + 3 i - i^{2} = - i^{2} + 2 i + 3$ Combine like terms: $3 - 3 i + i - i^{2} = - i^{2} - 2 i + 3$
③	$- i^{2} = - (- 1) = 1$ $- i^{2} = - (- 1) = 1$
④	Combine like terms: $1 + 2 i + 3 = 2 i + 4$ Combine like terms: $1 - 2 i + 3 = - 2 i + 4$
⑤	Remove the parentheses by changing the sign of each term within them. $- (- 2 i + 4) = 2 i - 4$
⑥	Combine like terms: $2 i + 4 + 2 i - 4 = 4 i$

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(1+i)⋅(3−i)−(3+i)⋅(1−i)=4i

$(1 + i) \cdot (3 - i) - (3 + i) \cdot (1 - i) = 4 i$