# How do you simplify (6i)^3?

Aug 12, 2016

${\left(6 i\right)}^{3} = - 216 i$

#### Explanation:

The most important thing to remember for doing any mathematical operations involving complex numbers is to treat $i$ as a variable, but i×i=i^2=-1.

Hence, i^3=i^2×i=-1×i=-i and ${i}^{4} = {\left({i}^{2}\right)}^{2} = {\left(- 1\right)}^{2} = 1$.

And (6i)^3=6^3×i^3

= 216×(-i)=-216i