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Question

Answer

$\frac{1 - 4 i - ( 2 + 4 i ) \cdot ( - 3 - i )}{4} - 1 = \frac{10 i - 1}{4}$

Explanation

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$\frac{1 - 4 i - ( 2 + 4 i ) \cdot ( - 3 - i )}{4} - 1 \overset{◯}{1} \frac{1 - 4 i - ( - 6 - 2 i - 12 i - 4 i ^{2} )}{4} - 1 \overset{◯}{2} \frac{1 - 4 i - ( - 4 i ^{2} - 14 i - 6 )}{4} - 1 \overset{◯}{3} \frac{1 - 4 i - ( 4 - 14 i - 6 )}{4} - 1 \overset{◯}{4} \frac{1 - 4 i - ( - 14 i - 2 )}{4} - 1 \overset{◯}{5} \frac{1 - 4 i + 14 i + 2}{4} - 1 \overset{◯}{6} \frac{10 i + 3}{4} - 1 \overset{◯}{7} \frac{10 i - 1}{4}$
①	Multiply each term of $(2 + 4 i)$ by each term in $(- 3 - i)$ . $(2 + 4 i) \cdot (- 3 - i) = - 6 - 2 i - 12 i - 4 i^{2}$
②	Combine like terms: $- 6 - 2 i - 12 i - 4 i^{2} = - 4 i^{2} - 14 i - 6$
③	$- 4 i^{2} = - 4 \cdot (- 1) = 4$
④	Combine like terms: $4 - 14 i - 6 = - 14 i - 2$
⑤	Remove the parentheses by changing the sign of each term within them. $- (- 14 i - 2) = 14 i + 2$
⑥	Combine like terms: $1 - 4 i + 14 i + 2 = 10 i + 3$
⑦	Subtract $1$ from $\frac{10 i + 3}{4}$ to get $\frac{10 i - 1}{4}$ . Step 1: Write $1$ as a fraction by putting $1$ in the denominator. Step 2: To subtract raitonal expressions, both fractions must have the same denominator. We can create a common denominator by multiplying the second fraction by $4$ . $\frac{10 i + 3}{4} - 1 Step 1 \frac{10 i + 3}{4} - \frac{1}{1} = \frac{10 i + 3}{4} - \frac{1 \cdot 4}{1 \cdot 4} = Step 2 \frac{10 i + 3}{4} - \frac{4}{4} = \frac{10 i - 1}{4}$

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