# How do you simplify (3+10i)^2 and write the complex number in standard form?

Aug 12, 2018

$- 91 + 60 i$

#### Explanation:

${\left(3 + 10 i\right)}^{2}$

$\left(3 + 10 i\right) \left(3 + 10 i\right)$

Use FOIL to distribute/expand:
$3 \cdot 3 = 9$

$3 \cdot 10 i = 30 i$

$10 i \cdot 3 = 30 i$

$10 i \cdot 10 i = 100 {i}^{2}$

Combine them together:
$9 + 30 i + 30 i + 100 {i}^{2}$

Combine like terms:
$9 + 60 i + 100 {i}^{2}$

We know that ${i}^{2} = - 1$, so:
$9 + 60 i + 100 \left(- 1\right)$

$= 9 + 60 i - 100$

$- 91 + 60 i$

We know standard form is $a + b i$ and this expression matches the form, so we are done.

Hope this helps!