Question

Simply the complex numbers. Express your answer in a+bi form and include each step necessary in simplifying.

3-2i
___
1+4i

Answer 1

When dividing complex numbers, we multiplicate both numerator and denominator by the conjugate of the denominator, like this:

Let:

z' = 1 - 4i (conjugate)

So:


`(3 - 2i)/(1 + 4i) . (1 - 4i)/(1 - 4i)`


`(3 - 12i - 2i + 8i^2)/(1 - 4i + 4i - 16i^2)`


`(3 - 14i + 8( √(-1))^2 )/(1 - 16( √(-1))^2 )`


`(3 - 14i + 8(-1))/(1 - 16(-1))`


`(3 - 14i - 8)/(1 + 16)`


`(- 5 - 14i)/(17)`

It's done, all steps have been made.

Hope it helps.