QuestionDecember 12, 2025

Watch the video and then solve the problem given below Click here to watch the video Divide (5+8i)/(9+6i) (5+8i)/(9+6i)=square (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in the form a+bi )

Watch the video and then solve the problem given below Click here to watch the video Divide (5+8i)/(9+6i) (5+8i)/(9+6i)=square (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in the form a+bi )
Watch the video and then solve the problem given below
Click here to watch the video
Divide
(5+8i)/(9+6i)
(5+8i)/(9+6i)=square 
(Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in the form a+bi )

Solution
4.4(212 votes)

Answer

\frac{93}{117} + \frac{42}{117}i Explanation 1. Multiply numerator and denominator by the conjugate of the denominator The conjugate of 9+6i is 9-6i. Multiply both numerator and denominator by 9-6i. 2. Expand numerator using distributive property (5+8i)(9-6i) = 5 \times 9 + 5 \times (-6i) + 8i \times 9 + 8i \times (-6i) = 45 - 30i + 72i - 48i^2 3. Simplify numerator using i^2 = -1 -48i^2 = -48(-1) = 48, so numerator becomes 45 - 30i + 72i + 48 = (45 + 48) + (-30i + 72i) = 93 + 42i 4. Expand denominator using difference of squares (9+6i)(9-6i) = 9^2 - (6i)^2 = 81 - 36i^2 5. Simplify denominator using i^2 = -1 -36i^2 = -36(-1) = 36, so denominator becomes 81 + 36 = 117 6. Write final answer in a+bi form \frac{93 + 42i}{117} = \frac{93}{117} + \frac{42}{117}i

Explanation

1. Multiply numerator and denominator by the conjugate of the denominator<br /> The conjugate of $9+6i$ is $9-6i$. Multiply both numerator and denominator by $9-6i$.<br />2. Expand numerator using distributive property<br /> $(5+8i)(9-6i) = 5 \times 9 + 5 \times (-6i) + 8i \times 9 + 8i \times (-6i) = 45 - 30i + 72i - 48i^2$<br />3. Simplify numerator using $i^2 = -1$<br /> $-48i^2 = -48(-1) = 48$, so numerator becomes $45 - 30i + 72i + 48 = (45 + 48) + (-30i + 72i) = 93 + 42i$<br />4. Expand denominator using difference of squares<br /> $(9+6i)(9-6i) = 9^2 - (6i)^2 = 81 - 36i^2$<br />5. Simplify denominator using $i^2 = -1$<br /> $-36i^2 = -36(-1) = 36$, so denominator becomes $81 + 36 = 117$<br />6. Write final answer in $a+bi$ form<br /> $\frac{93 + 42i}{117} = \frac{93}{117} + \frac{42}{117}i$
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