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Linear Algebra With Applications
Found in: Page 437
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

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

The period is 2ττ3.

See the step by step solution

Step by Step Solution

Step1: Euler’s formula:

The Euler’s formula is eit=cos t+i sin t

Step2: Explanation of the solution

Consider the given complex valued function:


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


Step3: Graphical representation of the solution

The function is sketched in figure 1 as follows.

Hence, the period for the function z=e3it is 2ττ3.

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