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Mathematics LibreTexts

6.4: Exercises- Complex Numbers, Vectors, and Functions

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Exercise 6.4.1

Express |ez| in terms of x and/or y.

Exercise 6.4.2

Confirm that eln(z)=z and ln(ez)=z

Exercise 6.4.3

Find the real and imaginary parts of cos(z) and sin(z)

Exercise 6.4.4

Show that cos2(z)+sin2(z)=1

Exercise 6.4.5

With zwewln(z) for complex z and w compute i

Exercise 6.4.6

Verify that cos(z) and sin(z) satisfy the Cauchy-Riemann equations and use the proposition to evaluate their derivatives.

Exercise 6.4.7

Submit a Matlab diary documenting your use of residue in the partial fraction expansion of the transfer function of

B=(200140012)


This page titled 6.4: Exercises- Complex Numbers, Vectors, and Functions is shared under a CC BY 1.0 license and was authored, remixed, and/or curated by Steve Cox via source content that was edited to the style and standards of the LibreTexts platform.

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