Question

I need help with this practice problem solving It asks to answer by in filling in the four boxes

Answer 1

The polar form of a complex number a + ib is given by:

$r\cdot cis(\theta)$$\begin{gathered} \text{ Where} \\ r=\sqrt{a^2+b^2} \\ \theta=\arctan(\frac{b}{a}) \end{gathered}$

In this case,

$\begin{gathered} a=2\sqrt{3} \\ b=-2 \end{gathered}$

Therefore,

$r=\sqrt{(2\sqrt{3})^2+(-2)^2}=\sqrt{12+4}=\sqrt{16}=4$

and

$\begin{gathered} \theta=\arctan(-\frac{2}{2\sqrt{3}})=\arctan(-\frac{1}{\sqrt{3}})=330^{\circ} \\ in\text{ radians} \\ \theta=\frac{11\pi}{6}\text{ radians} \end{gathered}$

The root is given by:

$undefined$