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

Dec 18, 2015

Foil the binomials.

$\left(2 + 7 i\right) \left(2 - 7 i\right) = 4 - 14 i + 14 i - 49 {i}^{2}$

$= 4 - 49 {i}^{2}$

However, you can rewrite $49 {i}^{2}$. It's very important to note that ${i}^{2} = - 1$ because $i = \sqrt{- 1}$.

$= 4 - 49 \left(- 1\right) = 4 + 49 = 53$

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