De Moivre's theorem and exponential form

De Moivre's theorem and exponential form Quiz

Spec 2.8–9 · Edexcel A-Level Further Maths: Quiz

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  1. 1. Find (cos⁡π8+isin⁡π8)4\left(\cos\frac{\pi}{8}+i\sin\frac{\pi}{8}\right)^4.

    • A. −1-1
    • B. 11
    • C. ii
    • D. −i-i

  2. 2. If z=cos⁡θ+isin⁡θz=\cos\theta+i\sin\theta, what is z+1zz+\frac1z?

    • A. 2cos⁡θ2\cos\theta
    • B. 2isin⁡θ2i\sin\theta
    • C. cos⁡θ\cos\theta
    • D. 22

  3. 3. Find 3eiπ/3×2eiπ/63e^{i\pi/3}\times2e^{i\pi/6}.

    • A. 5eiπ/25e^{i\pi/2}
    • B. 6eiπ/186e^{i\pi/18}
    • C. 6eiπ/66e^{i\pi/6}
    • D. 6eiπ/26e^{i\pi/2}

  4. 4. If z=cos⁡θ+isin⁡θz=\cos\theta+i\sin\theta, what is z2+z−2z^2+z^{-2}?

    • A. 2cos⁡θ2\cos\theta
    • B. 2cos⁡2θ2\cos2\theta
    • C. 2isin⁡2θ2i\sin2\theta
    • D. 2cos⁡2θ2\cos^2\theta

  5. 5. Which expression is sin⁡θ\sin\theta in exponential form?

    • A. 12(eiθ+e−iθ)\frac12\left(e^{i\theta}+e^{-i\theta}\right)
    • B. 12(eiθ−e−iθ)\frac12\left(e^{i\theta}-e^{-i\theta}\right)
    • C. 12i(eiθ−e−iθ)\frac{1}{2i}\left(e^{i\theta}-e^{-i\theta}\right)
    • D. 2i(eiθ−e−iθ)2i\left(e^{i\theta}-e^{-i\theta}\right)

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