Question

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

Answer 1

So I assume

`(5)/(4-3i)`

If so. Let us begin.


`\mathrm{Multiply\:by\:the\:conjugate}\:(4+3i)/(4+3i) \ \textgreater \ (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`


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


`Group\:the\:real\:part\:and\:the\:imaginary\:part\:of\:the\:complex\:number`

`(4)/(5)+(3)/(5)i\;is\;our\;answer!`

Hope this helps!