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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the expression for z^2 if z = 3e^(iπ/6)?
💡 Hint: Remember to square the modulus.
Question 2
Easy
Find the modulus of the complex number z = 1 + i.
💡 Hint: Use Pythagorean theorem!
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 complex power?
- z^n = r^n e^(inθ)
- z^n = r^n e^(θ)
- z^n = re^(nθ)
💡 Hint: Consider how the power affects both magnitude and direction.
Question 2
True or False: The nth roots of a complex number are always positioned randomly.
- True
- False
💡 Hint: Think about symmetry in their distribution.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Find all sixth roots of the complex number z = 64e^(iπ).
💡 Hint: Remember to divide the angle by 6 and account for the full rotation with 2π.
Question 2
Solve for z^n = (1 + i) where n = 3 using exponentials.
💡 Hint: Expressing initially in polar form simplifies the process.
Challenge and get performance evaluation