Question

How do you simplify `(2+7i)(2-7i)` and write in a+bi form?

Answer 1

Foil the binomials.

`(2+7i)(2-7i)=4-14i+14i-49i^2`

`=4-49i^2`

However, you can rewrite `49i^2`. It's very important to note that `i^2=-1` because `i=sqrt(-1)`.

`=4-49(-1)=4+49=53`

The answer is just `53`, which could also be written as `53+0i`.