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Chapter 9: Q5E (page 437)

Sketch the trajectory of the complex-valued function z=e(-0.1-2i)t.

Short Answer

Expert verified

The trajectory is in the inward spiral in the clockwise direction.

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 as follows:

z=e0.1-2it

Rewrite the function as follows:

Z=e(0.1+2i)Z=e-0.1te-2it

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

z=e-0.1te-2itz=e-0.1tcos-2t+isin-2tz=e-0.1tcos2t-isin2tz=e-0.1tcos2t-isin2t

03

Graphical representation of the solution

The trajectory of the function is sketched in figure 2 as follows:

Hence, the trajectory of z=e-0.1t(cos(2t)-isin(2t))is in the inward spiral in the clockwise direction.

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