Question

In Problems $11-22$, plot each complex number in the complex plane and write it in polar form. Express the argument in degrees.

$-2$

Short answer

The plot is

The polar form is$z=2\left(\cos 180°+i\sin 180°\right)$

Step-by-step solution

Step 1. Given information

Complex number is given as$-2$

Step 2. Plotting point 

Let $x=-2\&y=0$

Therefore the graph is

Step 3. Conversion to polar form

The radius is

$$\begin{gathered} r=\sqrt{x^2+y^2} \\ =\sqrt{(-2{)}^2+(0{)}^2} \\ =2 \end{gathered}$$

And the argument is

$$\begin{gathered} \theta ={\tan }^{-1}\left(\frac{y}{x}\right) \\ ={\tan }^{-1}\left(\frac{0}{-2}\right) \\ \left.=180°\text{(as}0\le \theta <360°\right) \end{gathered}$$

The polar coordinates is $(2,{180}^{\circ })$

The polar form is$z=2\left(\cos 180°+i\sin 180°\right)$