Question

write in the form of a+ib ​

Answer 1

IT TAKE MANY TIME TO TYPE

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Expand Exponent

$\underline{(2 + 3i). \frac{2 + 3i}{(4 + - 5i) {}^{3} } }$

Break up fraction.

$\underline{(2 + 3i).( \frac{2}{4 + - 5i) {}^{3} } + 3 \frac{i}{(4 + - 5i) {}^{3} }}$

Expand Exponent.

$\underline{(2 + 3i).( \frac{2}{(4 + - 5i).(4 + - 5i).(4 + - 5i)} + 3 \frac{i}{(4 + - 5i) {}^{3} } }$

Distribute

$\underline{(2 + 3i).( \frac{2}{(16 + - 20i + - 20i + 25i {}^{2} ).(4 + - 5i)} + \frac{i}{(4 + - 5i) {}^{3} } }$

Collect and combine like terms.

$\underline{(2 + 3i).( \frac{2}{(25i {}^{2} + - 40i + 16).(4 + - 5i) } + 3 \frac{i}{(4 + - 5i) {}^{3} } )}$

Distribute