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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
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!
Question 2
Easy
What is the principal value of the logarithm for z = 2e^(iπ)?
💡 Hint: Consider the angle for the principal value!
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the formula for the complex logarithm?
💡 Hint: Think of the polar form of a complex number.
Question 2
True or False: The complex logarithm is a single-valued function.
💡 Hint: Remember the periodic properties of complex exponentials.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation