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Course by: Steven J. Cox. E-mail the author

# Exercises: Complex Numbers, Vectors, and Functions

Module by: Steven J. Cox. E-mail the author

Summary: These are exercises to practice topics covered in modules regarding complex numbers, vectors, matrices, complex functions, and complex differentiation.

## Exercises

### Exercise 1

Express |ez| z in terms of xx and/or yy.

#### Solution

Pending completion of assignment.

### Exercise 2

Confirm that elnz=z z z and lnez=z z z .

#### Solution

Pending completion of assignment.

### Exercise 3

Find the real and imaginary parts of coszz and sinzz. Express your answers in terms of regular and hyperbolic trigonometric functions.

#### Solution

Pending completion of assignment.

### Exercise 4

Show that cos2z+sin2z=1 z 2 z 2 1

#### Solution

Pending completion of assignment.

### Exercise 5

With zwewlnz z w w z for complex zz and ww compute i

#### Solution

Pending completion of assignment.

### Exercise 6

Verify that coszz and sinzz satisfy the Cauchy-Riemann equations and use the proposition to evaluate their derivatives.

#### Solution

Pending completion of assignment.

### Exercise 7

Submit a Matlab diary documenting your use of residue in the partial fraction expansion of the transfer function of B=( 200 -140 0-12 ) B 2 0 0 -1 4 0 0 -1 2 .

#### Solution

Pending completion of assignment.

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