Question

Which fraction do you multiply by to simplify 5/ 4 - 3i ?

Answer 1

So I assume
$\frac{5}{4-3i}$

If so. Let us begin.

$\mathrm{Multiply\:by\:the\:conjugate}\:\frac{4+3i}{4+3i} \ \textgreater \ \frac{5\left(4+3i\right)}{\left(4-3i\right)\left(4+3i\right)} \ \textgreater \ \left(4-3i\right)\left(4+3i\right)$

$\mathrm{Apply\:complex\:arithmetic\:rule}:\ \left(a+bi\right)\left(a-bi\right)=a^2+b^2$
$Where\;a=4,\:b=-3 \ \textgreater \ 4^2+\left(-3\right)^2 \ \textgreater \ Refine \ \textgreater \ 25$

$\frac{5\left(4+3i\right)}{25} \ \textgreater \ \mathrm{Cancel\:the\:common\:factor:}\:5 \ \textgreater \ \frac{4+3i}{5}$

$Group\:the\:real\:part\:and\:the\:imaginary\:part\:of\:the\:complex\:number$
$\frac{4}{5}+\frac{3}{5}i\;is\;our\;answer!$

Hope this helps!