Question

How do you write `(a-bi)/(c+di)` in standard form?

Answer 1

`(a-bi)/(c+di) = (ac-bd)/(c^2+d^2)-(ad+bc)/(c^2+d^2)i`

Explanation:

`(a-bi)/(c+di) = ((a-bi)(c-di))/((c+di)(c-di))`

`color(white)((a-bi)/(c+di)) = ((ac-bd)-(ad+bc)i)/(c^2+d^2)`

`color(white)((a-bi)/(c+di)) = (ac-bd)/(c^2+d^2)-(ad+bc)/(c^2+d^2)i`