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Question

Answer

$3 \cdot \frac{40 - i \cdot 70 + i \cdot 50}{50 + 3 \cdot ( 40 - i \cdot 70 )} = \frac{15 i + 33}{73}$

Explanation

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$3 \cdot \frac{40 - i \cdot 70 + i \cdot 50}{50 + 3 \cdot ( 40 - i \cdot 70 )} \overset{◯}{1} 3 \cdot \frac{40 - i \cdot 70 + i \cdot 50}{50 + 120 - 210 i} \overset{◯}{2} \overset{◯}{3} 3 \cdot \frac{- 20 i + 40}{- 210 i + 170} \overset{◯}{4} 3 \cdot \frac{11 + 5 i}{73} \overset{◯}{5} \frac{15 i + 33}{73}$
①	Multiply $3$ by $(40 - 70 i)$ $3 \cdot (40 - 70 i) = 120 - 210 i$
②	Combine like terms: $40 - 70 i + 50 i = - 20 i + 40$
③	Combine like terms: $50 + 120 - 210 i = - 210 i + 170$
④	Divide $40 - 20 i$ by $170 - 210 i$ to get $\frac{11 + 5 i}{73}$ . ( view steps )
⑤	Multiply $3$ by $\frac{11 + 5 i}{73}$ to get $\frac{15 i + 33}{73}$ . Step 1: Write $3$ as a fraction by putting $1$ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $3 \cdot \frac{11 + 5 i}{73} Step 1 \frac{3}{1} \cdot \frac{11 + 5 i}{73} Step 2 \frac{3 \cdot ( 11 + 5 i )}{1 \cdot 73} = Step 3 \frac{33 + 15 i}{73} = \frac{15 i + 33}{73}$

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