Chapter 14, Problem 7CR

To determine

To find:The correct option.

Answer to Problem 7CR

The correct answer is (d).

Explanation of Solution

Given:

  $2-2i\sqrt{3}$

Calculation:

The general formula is given as,

  $\begin{array}{l}r=\pm \sqrt{x^2+y^2}\\ x=r\cos \theta \\ y=r\sin \theta \end{array}$

Calculate r.

  $\begin{array}{c}r=\sqrt{2^2+{\left(-2\sqrt{3}\right)}^2}\\ =\sqrt{4+12}\\ =\sqrt{16}\\ =4\end{array}$

Calculate $\sin \theta$

  $\begin{array}{c}\sin \theta =\frac{y}{r}\\ =\frac{-2\sqrt{3}}{4}\\ =-0.8660\end{array}$

The value of angle in fourth quadrant angle is,

  $\begin{array}{c}\theta =360-60\\ =300\end{array}$

Hence, $2-2i\sqrt{3}=4\left(\cos 300+i\sin 300\right)$

Thus, the correct answer is (d).