Question

Simplify the complex number. Express your answer in a + bi form and include each step necessary in simplifying./tex.z-dn.net/?f=%20%5Cfrac%7B3-2i%7D%7B1%2B4i%7D%20" id="TexFormula1" title=" \frac{3-2i}{1+4i} " alt=" \frac{3-2i}{1+4i} " align="absmiddle" class="latex-formula">

Answer 1

$\dfrac{x+iy}{u+iv}\times\dfrac{u-iv}{u-iv}=\dfrac{(x+iy)(u-iv)}{u^2-(iv)^2}$
$=\dfrac{xu-i^2yv+iyu-ixv}{u^2+v^2}$
$=\underbrace{\dfrac{xu+yv}{u^2+v^2}}_a+i\underbrace{\dfrac{yu-xv}{u^2+v^2}}_b$