Answer
$6i$
Work Step by Step
First, we use the product theorem to multiply the absolute values and add the arguments:
$(\sqrt{6} cis 120^{\circ})(\sqrt{6} cis (-30^{\circ}))
\\=\sqrt{6}\sqrt{6} cis (120^{\circ}-30^{\circ})
\\=6 cis (90^{\circ})$
Next, we change the expression into its equivalent form:
$=6 cis (90^{\circ})
\\6(\cos90^{\circ}+i\sin90^{\circ})$
Since we know that $\cos90^{\circ}=0$ and $\sin90^{\circ}=1$, we substitute these values in the expression and simplify:
$6(\cos90^{\circ}+i\sin90^{\circ})
\\=6(i)
\\=6i$
