# How do you simplify (1+4i)^2?

Dec 27, 2016

$- 15 + 8 i$

#### Explanation:

First, you can expand the square of the bynomial:

${\left(1 + 4 i\right)}^{2} = 1 + 8 i + 16 {i}^{2}$

Since ${i}^{2} = - 1$

the given expression becomes:

$1 + 8 i - 16 = - 15 + 8 i$