$(1 + i) \cdot (- 2 - i) \cdot (- 2 + 3 i) \frac{- 4 + i}{- 8 i \cdot ( - 4 + 2 i ) \cdot ( 1 - i ) \cdot ( 1 + 3 i ) \cdot ( 2 + i )} = \frac{- 95 i - 45}{800}$

Explanation

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①	Multiply each term of $(1 + i)$ by each term in $(- 2 - i)$ . $(1 + i) \cdot (- 2 - i) = - 2 - i - 2 i - i^{2}$
②	Combine like terms: $- 2 - i - 2 i - i^{2} = - i^{2} - 3 i - 2$
③	$- i^{2} = - (- 1) = 1$
④	Combine like terms: $1 - 3 i - 2 = - 3 i - 1$
⑤	Multiply each term of $(- 3 i - 1)$ by each term in $(- 2 + 3 i)$ . $(- 3 i - 1) \cdot (- 2 + 3 i) = 6 i - 9 i^{2} + 2 - 3 i$
⑥	Combine like terms: $6 i - 9 i^{2} + 2 - 3 i = - 9 i^{2} + 3 i + 2$
⑦	$- 9 i^{2} = - 9 \cdot (- 1) = 9$
⑧	Combine like terms: $9 + 3 i + 2 = 3 i + 11$
⑨	Multiply $8 i$ by $(- 4 + 2 i)$ $8 i \cdot (- 4 + 2 i) = - 32 i + 16 i^{2}$
⑩	$16 i^{2} = 16 \cdot (- 1) = - 16$
⑪	Multiply each term of $(- 32 i - 16)$ by each term in $(1 - i)$ . $(- 32 i - 16) \cdot (1 - i) = - 32 i + 32 i^{2} - 16 + 16 i$
⑫	Combine like terms: $- 32 i + 32 i^{2} - 16 + 16 i = 32 i^{2} - 16 i - 16$
⑬	$32 i^{2} = 32 \cdot (- 1) = - 32$
⑭	Combine like terms: $- 32 - 16 i - 16 = - 16 i - 48$
⑮	Multiply each term of $(- 16 i - 48)$ by each term in $(1 + 3 i)$ . $(- 16 i - 48) \cdot (1 + 3 i) = - 16 i - 48 i^{2} - 48 - 144 i$
⑯	Combine like terms: $- 16 i - 48 i^{2} - 48 - 144 i = - 48 i^{2} - 160 i - 48$
⑰	$- 48 i^{2} = - 48 \cdot (- 1) = 48$
⑱	Combine like terms: $48 - 160 i - 48 = - 160 i$
⑲	Multiply $- 160 i$ by $(2 + i)$ $- 160 i \cdot (2 + i) = - 320 i - 160 i^{2}$
⑳	$- 160 i^{2} = - 160 \cdot (- 1) = 160$
⑴	Divide $- 4 + i$ by $160 - 320 i$ to get $\frac{- 6 - 7 i}{800}$ . ( view steps )
⑵	Multiply $3 i + 11$ by $\frac{- 6 - 7 i}{800}$ to get $\frac{- 21 i ^{2} - 95 i - 66}{800}$ . Step 1: Write $3 i + 11$ as a fraction by putting $1$ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $3 i + 11 \cdot \frac{- 6 - 7 i}{800} Step 1 \frac{3 i + 11}{1} \cdot \frac{- 6 - 7 i}{800} Step 2 \frac{( 3 i + 11 ) \cdot ( - 6 - 7 i )}{1 \cdot 800} = Step 3 \frac{- 18 i - 21 i ^{2} - 66 - 77 i}{800} = \frac{- 21 i ^{2} - 95 i - 66}{800}$
⑶	$- 21 i^{2} = - 21 \cdot (- 1) = 21$
⑷	Simplify numerator $21 - 95 i - 66 = - 95 i - 45$

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(1+i)⋅(−2−i)⋅(−2+3i)−8i⋅(−4+2i)⋅(1−i)⋅(1+3i)⋅(2+i)−4+i​=800−95i−45​

$(1 + i) \cdot (- 2 - i) \cdot (- 2 + 3 i) \frac{- 4 + i}{- 8 i \cdot ( - 4 + 2 i ) \cdot ( 1 - i ) \cdot ( 1 + 3 i ) \cdot ( 2 + i )} = \frac{- 95 i - 45}{800}$