Chapter 12.7, Problem 29E

To determine

To find: the exponential form of each complex number.

Answer to Problem 29E

  $5e^{i\frac{5\pi }{3}}$

Explanation of Solution

Given information:

  $5\left(\cos \frac{5\pi }{3}+i\sin \frac{5\pi }{3}\right)$

Calculation:

Use $\cos x+i\sin x=e^{ix}$ to convert the complex number into exponential form as follows:

  $5\left(\cos \frac{5\pi }{3}+i\sin \frac{5\pi }{3}\right)=5e^{i\frac{5\pi }{3}}$

Thus, the value is $5e^{i\frac{5\pi }{3}}$ .