Answer
The result in the standard form is $8$.
Work Step by Step
Perform the standard operation and expand the given expression as below:
$\left( -1+i\sqrt{3} \right)\left( -1+i\sqrt{3} \right)\left( -1+i\sqrt{3} \right)$.
$\begin{align}
& =\,\left( -1+i\sqrt{3} \right)\left( 1-i\sqrt{3}-i\sqrt{3}+3{{i}^{2}} \right) \\
& =\left( -1+i\sqrt{3} \right)\left( 1-2i\sqrt{3}+3{{i}^{2}} \right) \\
& =\left( -1+i\sqrt{3} \right)\left( 1-2i\sqrt{3}-3 \right) \\
& =\left( -1+i\sqrt{3} \right)\left( -2-2i\sqrt{3} \right)
\end{align}$
Now, perform the multiplication operation again on the above reduced equation and simplify it as below:
$\begin{align}
& =\left( -1+i\sqrt{3} \right)\left( -2-2i\sqrt{3} \right) \\
& =\left( 2+2i\sqrt{3}-2i\sqrt{3}-6{{i}^{2}} \right) \\
& =2+6 \\
& =8 \\
\end{align}$
Therefore, the result in the standard form is $8$.
