Roots of complex numbers and roots of unity

Roots of complex numbers and roots of unity Quiz

Spec B10–B11 · AQA A-Level Further Maths: Quiz

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  1. 1. How many distinct fifth roots does the number −32-32 have?

    • A. 11
    • B. 44
    • C. 55
    • D. 1010

  2. 2. Which of these is a cube root of 88?

    • A. 2e2iπ/32\mathrm{e}^{2\mathrm{i}\pi/3}
    • B. 2eiπ/32\mathrm{e}^{\mathrm{i}\pi/3}
    • C. 8e2iπ/38\mathrm{e}^{2\mathrm{i}\pi/3}
    • D. 2eiπ/22\mathrm{e}^{\mathrm{i}\pi/2}

  3. 3. The solutions of z6=1z^6=1 are the vertices of which shape?

    • A. A square
    • B. A regular pentagon
    • C. An equilateral triangle
    • D. A regular hexagon

  4. 4. What is the sum of the nnth roots of unity for n≥2n\ge2?

    • A. nn
    • B. 00
    • C. 11
    • D. −1-1

  5. 5. One of the fifth roots of a complex number is 2eiπ/102\mathrm{e}^{\mathrm{i}\pi/10}. Another is:

    • A. 2eiπ/52\mathrm{e}^{\mathrm{i}\pi/5}
    • B. 2e2iπ/52\mathrm{e}^{2\mathrm{i}\pi/5}
    • C. 2eiπ/22\mathrm{e}^{\mathrm{i}\pi/2}
    • D. 2e−iπ/102\mathrm{e}^{-\mathrm{i}\pi/10}

Quiz