De Moivre's theorem and trigonometric identities

De Moivre's theorem and trigonometric identities Quiz

Spec 3.2 · Edexcel International A Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. (cos⁡θ+isin⁡θ)5=(\cos\theta+i\sin\theta)^5=

    • A. cos⁡5θ+isin⁡5θ\cos^5\theta+i\sin^5\theta
    • B. 5cos⁡θ+5isin⁡θ5\cos\theta+5i\sin\theta
    • C. cos⁡5θ+isin⁡5θ\cos5\theta+i\sin5\theta
    • D. cos⁡θ5+isin⁡θ5\cos\frac\theta5+i\sin\frac\theta5

  2. 2. (2eiπ/6)3=\left(2e^{i\pi/6}\right)^3=

    • A. 6i6i
    • B. 8i8i
    • C. 2i2i
    • D. 8eiπ/188e^{i\pi/18}

  3. 3. The imaginary part of (c+is)3(c+is)^3 is

    • A. 3c2s−s33c^2s-s^3
    • B. c3−3cs2c^3-3cs^2
    • C. 3cs2−s33cs^2-s^3
    • D. 3c2s+s33c^2s+s^3

  4. 4. z3+z−3z^3+z^{-3} for z=cos⁡θ+isin⁡θz=\cos\theta+i\sin\theta equals

    • A. 2isin⁡3θ2i\sin3\theta
    • B. 2cos⁡3θ2\cos^3\theta
    • C. 2cos⁡3θ2\cos3\theta
    • D. 22

  5. 5. Using (z−1z)2=−4sin⁡2θ\left(z-\frac1z\right)^2=-4\sin^2\theta and z2+z−2=2cos⁡2θz^2+z^{-2}=2\cos2\theta, sin⁡2θ=\sin^2\theta=

    • A. 12(1+cos⁡2θ)\frac12(1+\cos2\theta)
    • B. 1−cos⁡2θ1-\cos2\theta
    • C. 12cos⁡2θ\frac12\cos2\theta
    • D. 12(1−cos⁡2θ)\frac12(1-\cos2\theta)

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