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Complex Numbers

Simplify 4 ...

Question

Simplify $\frac{4 + 3 i}{5 - 3 i}$ .

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Solution

$\begin{matrix} \frac{4 + 3 i}{5 - 3 i} = \frac{4 + 3 i}{5 - 3 i} \times \frac{5 + 3 i}{5 + 3 i} = \frac{(4 + 3 i) (5 + 3 i)}{{(5)}^{2} - {(3 i)}^{2}} = \frac{20 + 27 i + 9 i^{2}}{25 - (- 9)} = \frac{11 + 27 i}{34} \end{matrix}$

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