Euler's relation and polar form

Euler's relation and polar form Quiz

Spec 3.1 · Edexcel International A Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. What is eiπ/2e^{i\pi/2}?

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

  2. 2. (3eiπ/4)(2eiπ/4)=\left(3e^{i\pi/4}\right)\left(2e^{i\pi/4}\right)=

    • A. 5eiπ/25e^{i\pi/2}
    • B. 6eiπ/26e^{i\pi/2}
    • C. 6eiπ/166e^{i\pi/16}
    • D. 6eiπ/46e^{i\pi/4}

  3. 3. 8eiπ/22eiπ/3=\dfrac{8e^{i\pi/2}}{2e^{i\pi/3}}=

    • A. 4eiπ/64e^{i\pi/6}
    • B. 4ei5π/64e^{i5\pi/6}
    • C. 16eiπ/616e^{i\pi/6}
    • D. 14eiπ/6\frac14e^{i\pi/6}

  4. 4. eiθ−e−iθ2i\dfrac{e^{i\theta}-e^{-i\theta}}{2i} is

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

  5. 5. −3+i-\sqrt3+i in the form reiθre^{i\theta}, with −π<θ≤π-\pi<\theta\le\pi, is

    • A. 2e−iπ/62e^{-i\pi/6}
    • B. 2e5πi/62e^{5\pi i/6}
    • C. 2eiπ/62e^{i\pi/6}
    • D. 4e5πi/64e^{5\pi i/6}

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