# What is (2 + square root of -3)(-1 + square root of -12)?

Sep 13, 2015

$- 8 + 3 i \sqrt{3}$

#### Explanation:

$\left(2 + \sqrt{- 3}\right) \left(- 1 + \sqrt{- 12}\right) \implies$ use:$i = \sqrt{- 1} \implies$

where i by definition is the imaginary part of a complex number:

$= \left(2 + i \sqrt{3}\right) \left(- 1 + i \sqrt{12}\right) \implies$simplify $\sqrt{12}$:

$= \left(2 + i \sqrt{3}\right) \left(- 1 + 2 i \sqrt{3}\right) \implies$expand:

$- 2 + 4 i \sqrt{3} - i \sqrt{3} + 2 {i}^{2} {\sqrt{3}}^{2} \implies$ simplify,note:${i}^{2} = - 1$:

$- 2 + 3 i \sqrt{s} 3 - 6 \implies$simplify:

$- 8 + 3 i \sqrt{3}$