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Question

Answer

$(\frac{80}{3} - 52.053 i) (\frac{80}{3} - 52.053 i) = \frac{- 24960 i - 17936}{9}$

Explanation

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$(\frac{80}{3} - 52.053 i) (\frac{80}{3} - 52.053 i) (\frac{80}{3} - 52 i) (\frac{80}{3} - 52 i) \overset{◯}{1} \overset{◯}{2} \frac{- 156 i + 80}{3} \frac{- 156 i + 80}{3} \overset{◯}{3} \frac{24336 i ^{2} - 24960 i + 6400}{9} \overset{◯}{4} \frac{- 24336 - 24960 i + 6400}{9} \overset{◯}{5} \frac{- 24960 i - 17936}{9}$
①	Subtract $52 i$ from $\frac{80}{3}$ to get $\frac{- 156 i + 80}{3}$ . Step 1: Write $52 i$ 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 $3$ . $\frac{80}{3} - 52 i Step 1 \frac{80}{3} - \frac{52 i}{1} = \frac{80}{3} - \frac{52 i \cdot 3}{1 \cdot 3} = Step 2 \frac{80}{3} - \frac{156 i}{3} = \frac{- 156 i + 80}{3}$
②	Subtract $52 i$ from $\frac{80}{3}$ to get $\frac{- 156 i + 80}{3}$ . Step 1: Write $52 i$ 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 $3$ . $\frac{80}{3} - 52 i Step 1 \frac{80}{3} - \frac{52 i}{1} = \frac{80}{3} - \frac{52 i \cdot 3}{1 \cdot 3} = Step 2 \frac{80}{3} - \frac{156 i}{3} = \frac{- 156 i + 80}{3}$
③	Multiply $\frac{- 156 i + 80}{3}$ by $\frac{- 156 i + 80}{3}$ to get $\frac{24336 i ^{2} - 24960 i + 6400}{9}$ . Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $\frac{- 156 i + 80}{3} \cdot \frac{- 156 i + 80}{3} Step 1 \frac{( - 156 i + 80 ) \cdot ( - 156 i + 80 )}{3 \cdot 3} = Step 2 \frac{24336 i ^{2} - 12480 i - 12480 i + 6400}{9} = \frac{24336 i ^{2} - 24960 i + 6400}{9}$
④	$24336 i^{2} = 24336 \cdot (- 1) = - 24336$
⑤	Simplify numerator $- 24336 - 24960 i + 6400 = - 24960 i - 17936$

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