Practice De Moivre’s Theorem (5.6) - Complex Exponential Function

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6 sample questions

Question 1.
Express (cos(30°) + isin(30°))^2 in terms of cosine and sine.
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Use the angle doubling property.
Question 2.
State De Moivre's Theorem.
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Recall the formula involving cosine and sine.
3Question 3.
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)
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Remember the relationship with powers and how angles are manipulated.
4Question 4.
True or False: De Moivre's Theorem applies only to real numbers.
- True
- False
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Think about where complex numbers come into play.
Question 5.
Using De Moivre's Theorem, compute (cos(30°) + i*sin(30°))^6 and provide the answer in rectangular form.
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Remember to multiply the angle accordingly.
Question 6.
Find all cube roots of the complex number 8 using De Moivre's Theorem and provide their polar forms.
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You can draw the roots on a circle in the complex plane.

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