Answer
$-1-\sqrt{3}i$
Work Step by Step
First, we use the division theorem to divide the absolute values and subtract the arguments:
$\frac{16(cis 310^{\circ})}{8(cis70^{\circ})}
\\=2cis(310^{\circ}-70^{\circ})
\\=2cis240^{\circ}$
Next, we change the expression into its equivalent form:
$=2 cis 240^{\circ}
\\=2(\cos240^{\circ}+i\sin240^{\circ})$
Since we know that $\cos240^{\circ}=-\frac{1}{2}$ and $\sin240^{\circ}=-\frac{\sqrt{3}}{2}$, we can substitute these values in the expression and simplify:
$2 (\cos240^{\circ}+i\sin240^{\circ})
\\=2(-\frac{1}{2}-\frac{\sqrt{3}}{2}i)
\\=-1-\sqrt{3}i$
