# How do you write (2+3i)^2 in standard form?

Dec 14, 2015

${\left(2 + 3 i\right)}^{2} = - 5 + 12 i$

#### Explanation:

Rewrite the expression as

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

Expand by multiplying the expression to get

$\left(4 + 6 i + 6 i + 9 {i}^{2}\right)$

Combine like terms

$\left(4 + 12 i + 9 {i}^{2}\right)$

Replace ${i}^{1} = - 1$ , this is be definition if imaginary number

$\left(4 + 12 i + 9 \cdot \left(- 1\right)\right) \implies 4 - 9 + 12 i \implies - 5 + 12 i$

${\left(2 + 3 i\right)}^{2} = - 5 + 12 i$