alleryIf z = cos(π/7) + i sin(π/7), then z⁷ equals:
- i
- -1
- 1
- -i
Show answer and solution
Correct answer: B. -1
By DeMoivre: z⁷ = (cos π/7 + i sin π/7)⁷ = cos(π) + i sin(π) = -1 + 0i = -1.
AP Intermediate 1st Year Unit 3B: Implicit Differentiation and Inverse Functions — practice questions
Explore 4 free Unit 3B: Implicit Differentiation and Inverse Functions questions in AP Intermediate 1st Year Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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If z = cos(π/7) + i sin(π/7), then z⁷ equals:Read the answer and worked solution →For complex z, |z + i| = |z - i| describes:Read the answer and worked solution →|z|² = z × z̄. If |z|² = 4 and Re(z) = 1, then Im(z):Read the answer and worked solution →Find principal argument of -1 - i:Read the answer and worked solution →
Worked practice questions
For complex z, |z + i| = |z - i| describes:
- A circle
- The real axis
- The imaginary axis
- Origin only
Show answer and solution
Correct answer: B. The real axis
Equidistant from i (= (0, 1)) and -i (= (0, -1)) means z lies on the perpendicular bisector — the real axis (y = 0).
|z|² = z × z̄. If |z|² = 4 and Re(z) = 1, then Im(z):
- ±√3
- √3
- 2
- ±2
Show answer and solution
Correct answer: A. ±√3
|z|² = a² + b² = 4. With a = 1: b² = 3, so b = ±√3.
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