Question

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divide and express the result in standard form.
\\(\frac{9 + 4i}{8 - 9i}=\\) enter your answer
note: show your result in the form (a + bi) and use reduced fractions where needed.
submit answer attempts: 0/1
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Explanation:

Step1: Multiply by conjugate

Multiply numerator and denominator by the conjugate of the denominator $8 + 9i$.
$\frac{9 + 4i}{8 - 9i}\times\frac{8 + 9i}{8 + 9i}$

Step2: Expand numerator

Use FOIL method: $(9 + 4i)(8 + 9i)=9\times8+9\times9i+4i\times8+4i\times9i=72 + 81i+32i + 36i^{2}$. Since $i^{2}=-1$, it becomes $72+81i + 32i-36=36 + 113i$.

Step3: Expand denominator

Use $(a - b)(a + b)=a^{2}-b^{2}$. Here, $(8 - 9i)(8 + 9i)=8^{2}-(9i)^{2}=64-81i^{2}=64 + 81 = 145$.

Step4: Write in standard form

$\frac{36 + 113i}{145}=\frac{36}{145}+\frac{113}{145}i$

Answer:

$\frac{36}{145}+\frac{113}{145}i$