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Chapter 9: Q4E (page 437)

Sketch the trajectory of the complex-valued function z=e3itand find its period.

Short Answer

Expert verified

The period is 2蟿蟿3.

Step by step solution

01

Euler’s formula:

The Euler鈥檚 formula iseit=cost+isint

02

Explanation of the solution

Consider the given complex valued function:

z=e3it

By using Euler鈥檚 formula, the function can be written as follows.

z=e3itZ=cos3t+isin3t

03

Graphical representation of the solution

The function is sketched in figure 1 as follows.

Hence, the period for the functionz=e3it is 2蟿蟿3.

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