# Evaluate: (1+sqrt(3)i) \times (1-sqrt(3)i)

## Expression: $\left( 1+\sqrt{ 3 }i \right) \times \left( 1-\sqrt{ 3 }i \right)$

Use $\left( a-b \right)\left( a+b \right)={a}^{2}-{b}^{2}$ to simplify the product

$1-3{i}^{2}$

By definition ${i}^{2}=-1$

$1-3 \times \left( -1 \right)$

Any expression multiplied by $-1$ equals its opposite

$1+3$

$4$