Applet Exploration: Complex Exponential
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Start by opening the Complex Exponential applet .
The Unit Circle
1. Set a = 0 and b = 1. As you change t notice that eibt always lies on
the unit circle. What happens if you change the value of b leaving a = 0?
Explain this in terms of sin and cos.
2. When you increase a from 0 what happens to the circle? Explain this by
expanding e(a+bi)t .