Chapter 14.4, Problem 17WE

To determine

To find: The given complex number in $x+yi$ form.

Answer to Problem 17WE

  $-1.9052+1.1000i$ .

Explanation of Solution

Given information:

A complex number in polar form is given as $2.2\left(\cos {150}^0+i\sin {150}^0\right)$ .

Concepts used: The polar form of a complex number $z=x+yi$ is given by −

  $z=r\left(\cos \theta +i\sin \theta \right)$

where $r=\sqrt{x^2+y^2},\cos \theta =\frac{x}{r},\sin \theta =\frac{y}{r}$ .

Calculation:

Given complex number in polar form is $2.2\left(\cos {150}^0+i\sin {150}^0\right)$ .

Converting into $x+yi$ form -

  $\begin{array}{l}2.2\left(\cos {150}^0+i\sin {150}^0\right)\\ =2.2\left(-0.8660+0.5i\right)\left\{{\text{Since, cos150}}^0=-0.8660,\sin {150}^0=0.5\right\}\\ =-1.9052+1.1000i\end{array}$

Hence, given complex number in desired form is $-1.9052+1.1000i$ .