Practice Complex Powers And Roots (5.12) - Complex Exponential Function
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Complex Powers and Roots

Practice - Complex Powers and Roots

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Practice Questions

Test your understanding with targeted questions

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!

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

Solve for z^n = (1 + i) where n = 3 using exponentials.

💡 Hint: Expressing initially in polar form simplifies the process.

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