Question

write
3+4 i÷
5-12i
in the
x +iy form , hence
find its
real
and imaginary parts.​

Answer 1

$\frac{3 + 4i}{5 - 12i} \times \frac{5 + 12i}{5 + 12i} = \\ \frac{(3 + 4i)(5 + 12i)}{(5 -12i)(5 +12i)} \\ = \frac{15 + 36i + 20i + 48 {i}^{2} }{ {5}^{2} - {12i}^{2}}$

$\frac{15 + 56i - 48}{25 + 144} = \frac{56i - 33}{169} \\ = \frac{56}{169}i - \frac{33}{169} \\imaginary \:part = \frac{56}{169}i \\ real \: part \: = - \frac{33}{169}$