Practice - Complex Powers and Roots
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Practice Questions
Test your understanding with targeted questions
What is the expression for z^2 if z = 3e^(iπ/6)?
💡 Hint: Remember to square the modulus.
Find the modulus of the complex number z = 1 + i.
💡 Hint: Use Pythagorean theorem!
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the formula for complex power?
💡 Hint: Consider how the power affects both magnitude and direction.
True or False: The nth roots of a complex number are always positioned randomly.
💡 Hint: Think about symmetry in their distribution.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
Solve for z^n = (1 + i) where n = 3 using exponentials.
💡 Hint: Expressing initially in polar form simplifies the process.
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Reference links
Supplementary resources to enhance your learning experience.