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=√(a^2+b^2) \\ \theta=\arctan((b)/(a)) \end{gathered}`

In this case,

`\begin{gathered} a=2√(3) \\ b=-2 \end{gathered}`

Therefore,

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

and

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

The root is given by: