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Argument of a complex number (often a quotient)

This type of question, asked 4 times: 9 May 2023 S1, 16 May 2023 S2, 10 May 2024 S2, 11 Apr 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    9 May 2023 S1

    140
    If Z=−21+3iZ=\frac{-2}{1+\sqrt{3}i}, i=−1i=\sqrt{-1}, then the value of arg⁡(Z)\arg(Z) is

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  2. Question 2

    16 May 2023 S2

    104
    If z1=5−2iz_1 = 5-2i and z2=3+iz_2 = 3+i, where i=−1i = \sqrt{-1}, then arg⁡(z1+z2z1−z2)\arg\left(\frac{z_1+z_2}{z_1-z_2}\right) is

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  3. Question 3

    10 May 2024 S2

    150
    The argument of 1+i33−i\dfrac{1+i\sqrt{3}}{\sqrt{3}-i}, i=−1i=\sqrt{-1}, is

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  4. Question 4

    11 Apr 2026 S1

    52
    If −1+−3=reiθ-1 + \sqrt{-3} = re^{i\theta}, then the value of θ\theta is

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