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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Express (cos(30°) + isin(30°))^2 in terms of cosine and sine.
💡 Hint: Use the angle doubling property.
Question 2
Easy
State De Moivre's Theorem.
💡 Hint: Recall the formula involving cosine and sine.
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 does De Moivre's Theorem state?
- (cosθ + isinθ)n = cos(nθ) + isin(nθ)
- (cosθ + isinθ)n = sin(nθ) + i cos(nθ)
- (cosθ + isinθ)n = e^(nθ)
💡 Hint: Remember the relationship with powers and how angles are manipulated.
Question 2
True or False: De Moivre's Theorem applies only to real numbers.
- True
- False
💡 Hint: Think about where complex numbers come into play.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Using De Moivre's Theorem, compute (cos(30°) + i*sin(30°))^6 and provide the answer in rectangular form.
💡 Hint: Remember to multiply the angle accordingly.
Question 2
Find all cube roots of the complex number 8 using De Moivre's Theorem and provide their polar forms.
💡 Hint: You can draw the roots on a circle in the complex plane.
Challenge and get performance evaluation