In order to write in form a + bi we must conjugate the denominator. In other words multiply both the numerator and denominator by the conjugate of (1+2i) which is (1 - 2i). It will look like this:

`1/(1+2i)* (1-2i)/(1-2i)` I can do this because this value is equivalent to 1. Multiplying by 1 does not change value of original expression.

Multiplying numerators gives me: `1 - 2i`

Multiplying denominators is the difference of 2 squares. (I can use foil in which middle terms cancel each other.)

`(1+2i)(1-2i) = 1 -2i + 2i - 4i^2`

Since `i^2` equals -1 this expression simplifys to `1 - (-4) = 5`

Therefore we have `(1-2i)/5`

**Written in a+bi form this is:** `1/5 -2/5i`

## We’ll help your grades soar

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now