Practice Logarithm Of A Complex Number (5.11) - Complex Exponential Function

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9 questions

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6 sample questions

Question 1.
Write the logarithm of the complex number z = 3e^(iπ/4) in its general form.
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Remember to express it in terms of modulus and argument!
Question 2.
What is the principal value of the logarithm for z = 2e^(iπ)?
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Consider the angle for the principal value!
3Question 3.
What is the formula for the complex logarithm?
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Think of the polar form of a complex number.
4Question 4.
True or False: The complex logarithm is a single-valued function.
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Remember the periodic properties of complex exponentials.
Question 5.
Prove that ln(z) = ln(r) + i(θ + 2πn) using the periodic property of complex exponentials.
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Start with the definition of the complex exponential.
Question 6.
Derive the principal value for ln(-1) and discuss its significance in engineering applications.
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Consider the angle that corresponds to -1 in the complex plane.

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