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

May 14, 2016

$- 5 + 12 i$

#### Explanation:

We can simply multiply this out like a binomial, remembering that ${i}^{2} = - 1$.

${\left(2 + 3 i\right)}^{2}$

$\implies \left(2 + 3 i\right) \left(2 + 3 i\right)$

$\implies 4 + 6 i + 6 i + 9 {i}^{2}$

$\implies 4 + 12 i - 9$

$\implies - 5 + 12 i$

NOTE this is different than the mod-squared of a complex number which is written $| z {|}^{2} = z \cdot \overline{z}$ where $\overline{z}$ is the complex conjugate of $z$.