Chapter 12, Problem 41SGA

To determine

To find: the exponential form of the given expression or complex number.

Answer to Problem 41SGA

  $2e^{i\frac{3\pi }{4}}$

Explanation of Solution

Given information:

  $2\left(\cos \frac{3\pi }{4}+i\sin \frac{3\pi }{4}\right)$

Calculation:

The exponential of the given expression can be evaluated as follows:

  $\begin{array}{c}\cos x+i\sin x=e^{ix}\\ 2\left(\cos \frac{3\pi }{4}+i\sin \frac{3\pi }{4}\right)=2e^{i\frac{3\pi }{4}}\left[\text{Let }x=\frac{3\pi }{4}\right]\end{array}$

Thus the exponential form is $2e^{i\frac{3\pi }{4}}$ .