Use De Moivre's theorem to write (1 + i)^6 in the form a + bi.
Answer and explanation
Correct answer: D. -8i
- Step 1: 1 + i = sqrt(2) cis(pi/4). Step 2. (1 + i)^6 = (sqrt 2)^6 cis(6pi/4) = 8 cis(3pi/2) = 8(0 - i) = -8i. Answer: -8i. Why not the others: 8i uses an angle of pi/2, -8 uses an angle of pi, and 8 uses an angle of 2pi; only 3pi/2 matches six lots of pi/4.
Practise more Complex Numbers, De Moivre's Theorem and Polynomial Theory.
Free questions with an explanation for every one, and full timed New Zealand Scholarship mock tests.
More Complex Numbers, De Moivre's Theorem and Polynomial Theory questions
- What is the modulus and principal argument of the complex number z = -1 + i*sqrt(3)?
- Using De Moivre's theorem, evaluate (1 + i)^8.
- If 2 - 3i is a root of the cubic equation x^3 - 3x^2 + 9x + 13 = 0 with real coefficients, what are the other two roots?
- What geometric locus is described by the equation |z - (2 + 3i)| = 5 in the complex Argand plane?
- What geometric locus is described by |z - 4| = |z + 2i| in the complex plane?
- What are the three cube roots of unity (solutions to z^3 = 1) in exponential form?