Elementary Functions

Practice Questions

Complex Analysis › Elementary Functions

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1

$|e^{Z^{2}}|\leq\ e^{|Z|^{2}}$

Is the above inequality true?

2

Find all values of such that... $e^{Z}=-2$

3

If $e^{Z}$ is pure imaginary what restriction is placed on ?

Eulersfunitc

hint: where is the only place(s) on the complex unit circle where is pure imaginary and what is the angle(s) that put you there.

4

What does $e^{Z+\pi i}$ equal?

5

$f(x+yi)=e^{x-yi}$

where in the complex plane does the above function satisfy the Cauchy-Riemann equations.

6

Compute $e^{\left(\frac{2+\pi i}{4}\right)}$

7

$e^{Z}=1+\sqrt{3}i$

Solve the above equation for all values of .

8

Eulersfunitc

Use the complex unit circle to find the value of $e^{i\pi /2}$

9

$f(Z)=e^{Z^{2}}$

$f(x+iy)=e^{(x+iy)^{2}}$

Where in the complex plane does the above function satisfy the Cauchy-Riemann equations.

10

Compute

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