# How do you multiply (3+5i)^2 ?

Jun 8, 2016

The answer is $- 16 + 30 i$

#### Explanation:

To square a complex number you do a similar action as if you were to square an expression like $\left(a + b x\right)$. The only difference is you have to remember that ${i}^{2} = - 1$

So:

${\left(3 + 5 i\right)}^{2} = {3}^{2} + 2 \cdot 3 \cdot 5 i + {\left(5 i\right)}^{2} = 9 + 30 i + 25 {i}^{2}$
$= 9 + 30 i \textcolor{red}{- 25} = 9 - 25 + 30 i = - 16 + 30 i$

The minus sign in the marked expression comes from the fact that ${i}^{2} = - 1$