5.11 - Logarithm of a Complex Number
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Practice Questions
Test your understanding with targeted questions
Write the logarithm of the complex number z = 3e^(iπ/4) in its general form.
💡 Hint: Remember to express it in terms of modulus and argument!
What is the principal value of the logarithm for z = 2e^(iπ)?
💡 Hint: Consider the angle for the principal value!
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the formula for the complex logarithm?
💡 Hint: Think of the polar form of a complex number.
True or False: The complex logarithm is a single-valued function.
💡 Hint: Remember the periodic properties of complex exponentials.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Prove that ln(z) = ln(r) + i(θ + 2πn) using the periodic property of complex exponentials.
💡 Hint: Start with the definition of the complex exponential.
Derive the principal value for ln(-1) and discuss its significance in engineering applications.
💡 Hint: Consider the angle that corresponds to -1 in the complex plane.
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