Question

How do you simplify `(1 + 2i) / (3-4i)`?

Answer 1

`-1/5+2/5i`

Explanation:

`"multiply the numerator/denominator by the "color(blue)"conjugate"`
`"of the denominator"`

`"this ensures that the denominator is real"`

`"the conjugate of "3-4i" is "3color(red)(+)4i`

`color(orange)"Reminder "color(white)(x)i^2=(sqrt(-1))^2=-1`

`rArr(1+2i)/(3-4i)xx(3+4i)/(3+4i)`

`=((1+2i)(3+4i))/((3-4i)(3+4i))larrcolor(blue)"expand using FOIL"`

`=(3+10i+8i^2)/(9-16i^2)`

`=(-5+10i)/25`

`=(-5)/25+10/25i`

`=-1/5+2/5ilarrcolor(red)"in standard form"`