Argand diagrams and modulus-argument form

Argand diagrams and modulus-argument form Quiz

Spec B4–B6 · AQA A-Level Further Maths: Quiz

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  1. 1. Find arg⁡(−2−2i)\arg(-2-2i) in (−π,π](-\pi,\pi].

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

  2. 2. z=2(cos⁡π6+isin⁡π6)z=2\left(\cos\frac{\pi}{6}+i\sin\frac{\pi}{6}\right) and w=3(cos⁡π3+isin⁡π3)w=3\left(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\right). Find zwzw.

    • A. 6i6i
    • B. 66
    • C. 5i5i
    • D. −6i-6i

  3. 3. Which is the modulus-argument form of −3-3?

    • A. 3(cos⁡0+isin⁡0)3(\cos0+i\sin0)
    • B. −3(cos⁡π+isin⁡π)-3(\cos\pi+i\sin\pi)
    • C. 3(cos⁡π+isin⁡π)3(\cos\pi+i\sin\pi)
    • D. 3(cos⁡π2+isin⁡π2)3\left(\cos\frac{\pi}{2}+i\sin\frac{\pi}{2}\right)

  4. 4. ∣z∣=10|z|=10, arg⁡z=π2\arg z=\frac{\pi}{2}, ∣w∣=2|w|=2, arg⁡w=π6\arg w=\frac{\pi}{6}. Find the modulus and argument of zw\frac{z}{w}.

    • A. Modulus 2020, argument 2π3\frac{2\pi}{3}
    • B. Modulus 55, argument π3\frac{\pi}{3}
    • C. Modulus 55, argument 2π3\frac{2\pi}{3}
    • D. Modulus 1212, argument π3\frac{\pi}{3}

  5. 5. The points PP and QQ represent 2+i2+i and 5+5i5+5i. Which complex number represents the vector PQ→\overrightarrow{PQ}?

    • A. 7+6i7+6i
    • B. −3−4i-3-4i
    • C. 3+4i3+4i
    • D. 10+5i10+5i

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