4+3i(2+3i)(4 3i) (4+3i)(4+3i)25(2+3i) 7+24i25(2+3i) (7+24i)(2 3i)25 × 13 14 21i+48i+72325 86+27i325 ...

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Complex Numbers

4+3i2+3i4-3i.

Question

$\frac{4 + 3 i}{(2 + 3 i) (4 - 3 i)}$ .

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Solution

$\frac{4 + 3 i}{(2 + 3 i) (4 - 3 i)}$
$\frac{(4 + 3 i) (4 + 3 i)}{25 (2 + 3 i)}$
$\frac{7 + 24 i}{25 (2 + 3 i)}$
$\frac{(7 + 24 i) (2 - 3 i)}{25 \times 13}$
$\frac{14 - 21 i + 48 i + 72}{325}$
$\frac{86 + 27 i}{325}$

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