1.14 Polynomial roots, De Moivre's theorem, powers and roots

1.14 Polynomial roots, De Moivre's theorem, powers and roots Quiz

IB Maths: Analysis and Approaches HL: Quiz

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  1. 1. A quartic with real coefficients has roots 1+i1 + i and 2i2i. Which of these is also a root?

    • A. −1+i-1 + i
    • B. −2i-2i
    • C. 1+2i1 + 2i
    • D. 22

  2. 2. Find (2eiπ/8)4(\sqrt{2}e^{i\pi/8})^{4}.

    • A. 4i4i
    • B. 44
    • C. 2i2i
    • D. 42i4\sqrt{2}i

  3. 3. What is the modulus of each root of z4=81iz^{4} = 81i?

    • A. 33
    • B. 8181
    • C. 814\frac{81}{4}
    • D. 99

  4. 4. The cube roots of −8-8 are 2eiθ2e^{i\theta}. Which is NOT a possible value of θ\theta?

    • A. π3\frac{\pi}{3}
    • B. π\pi
    • C. −π3-\frac{\pi}{3}
    • D. 2π3\frac{2\pi}{3}

  5. 5. Using De Moivre's theorem, sin⁡3θ\sin3\theta equals

    • A. 3sin⁡θ−4sin⁡3θ3\sin\theta - 4\sin^{3}\theta
    • B. 4sin⁡3θ−3sin⁡θ4\sin^{3}\theta - 3\sin\theta
    • C. 3sin⁡θ3\sin\theta
    • D. 3sin⁡θcos⁡2θ3\sin\theta\cos^{2}\theta

Quiz