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`