5.9. Real and Imaginary Parts of eix

Try these first

1. 1.

   What are the real and imaginary parts of e^{ix}?

   Hint

   Recall Euler's formula.

2. 2.

   State Euler's formula.

   Hint

   It's the relationship between complex exponentials and trigonometric functions.

3. 3.

   What is the real part of e^{ix}?

   • sin(x)
   • cos(x)
   • tan(x)

   Hint

   This can be found directly from Euler's formula.

4. 4.

   The imaginary part of e^{ix} is?

   • sin(x)
   • cos(x)
   • 1

   Hint

   Remember the components of Euler's formula.

5. 5.

   Given the complex signal e^(i(2πn)), where n is an integer, describe how the signal behaves as n changes.

   Hint

   Consider how often sine and cosine repeat.

6. 6.

   Using Fourier analysis, express a function with components a + b cos(x) + c sin(x) in the form of e^(ix). How would this aid in analysis?

   Hint

   Rewrite cos and sin using euler's formula.