Question

Divide the following complex numbers: (4-i)/(3+4i) ??

Answer 1

Given : $\frac{(4 - i)}{(3 + 4i)}$

Multiplying and Dividing with (3 - 4i)

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

$\implies \frac{(12 - 16i + 4i^2 - 3i)}{(9 - 16i^2)}$

We know that i² = -1

$\implies \frac{(12 - 19i - 4)}{(9 + 16)}$

$\implies \frac{8 - 19i}{25}$

$\implies \frac{8}{25} - \frac{19}{25}i$

Option D is the Answer