Practice Properties Of The Complex Exponential Function (5.3)

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6 sample questions

Question 1.
What is the modulus of e^{2 + 3i}?
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Remember the modulus only involves the real part.
Question 2.
Write down Euler's formula.
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Consider the relationship between exponential and trigonometric functions.
3Question 3.
What does the modulus of a complex exponential depend on?
- Real part
- Imaginary part
- Both parts
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Focus on the expression for modulus calculation.
4Question 4.
True or False: The derivative of the complex exponential function is equal to the function itself.
- True
- False
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Think about how derivatives work for exponential functions in general.
Question 5.
Prove that e^{(a+bi) + (c+di)} = e^{a+c} e^{(b+d)i} using the properties of complex exponentials.
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Start by expanding both sides according to exponential properties.
Question 6.
If |z| = e^3 and z has a negative imaginary part, what can we infer about its position in the complex plane?
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Remember how modulus functions dictate positioning in the complex plane.

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