Question

5+3i/5-3i in x+i y form​

Answer 1

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See the attachment please

Sorry, I did a mistake.

Now the answer is correct

Answer 2

$\frac{5 + 3i}{5 - 3i}$

Let's rationalize to get x + iy form

$= \frac{5 + 3i}{5 - 3i} \times \frac{5 + 3i}{5 + 3i}$

$= \frac{ {(5 + 3i)}^{2} }{ {5}^{2} - ( {3i)}^{2} }$

$= \frac{ {5}^{2} + ( {3i)}^{2} + 2 \times 5 \times 3i}{25 - {(3)}^{2} ( {i)}^{2} }$

$= \frac{25 + {3}^{2} {(i)}^{2} + 30i }{25 - 9 {(i)}^{2} }$

$= \frac{25 + 9( - 1) + 30i}{25 - 9( - 1)}$

$= \frac{25 - 9 + 30i}{25 + 9}$

$= \frac{16 + 30i}{34}$

$= \frac{16}{34} + \frac{30}{34} i \\ \\ = \frac{8}{17} + \frac{15}{17} i$

$x \: = \frac{8}{17} \\ \\ y = \frac{15}{17}$

$x + iy = ( \frac{8}{17} )+ i( \frac{15}{17} )$