Argand diagrams and modulus-argument form

Argand diagrams and modulus-argument form Quiz

Spec 2.4–6 · Edexcel A-Level Further Maths: Quiz

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  1. 1. What is the principal argument of −2+2i-2+2i?

    • A. −π4-\frac{\pi}{4}
    • B. π4\frac{\pi}{4}
    • C. 3π4\frac{3\pi}{4}
    • D. −3π4-\frac{3\pi}{4}

  2. 2. If ∣z1∣=3|z_1|=3 and ∣z2∣=5|z_2|=5, what is ∣z1z2∣|z_1z_2|?

    • A. 1515
    • B. 88
    • C. 35\frac35
    • D. 22

  3. 3. arg⁡z1=2π3\arg z_1=\frac{2\pi}{3} and arg⁡z2=π4\arg z_2=\frac{\pi}{4}. Find arg⁡z1z2\arg\frac{z_1}{z_2}.

    • A. 11π12\frac{11\pi}{12}
    • B. π26\frac{\pi^2}{6}
    • C. π3\frac{\pi}{3}
    • D. 5π12\frac{5\pi}{12}

  4. 4. Write 2(cos⁡π6+isin⁡π6)2\left(\cos\frac{\pi}{6}+i\sin\frac{\pi}{6}\right) in the form x+iyx+iy.

    • A. 1+i31+i\sqrt3
    • B. 3+i\sqrt3+i
    • C. 2+i22+\frac{i}{2}
    • D. 32+i2\frac{\sqrt3}{2}+\frac{i}{2}

  5. 5. What is the principal argument of −1−i-1-i?

    • A. −3π4-\frac{3\pi}{4}
    • B. 3π4\frac{3\pi}{4}
    • C. π4\frac{\pi}{4}
    • D. −π4-\frac{\pi}{4}

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