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  • Perplex
    IB Math AAHL
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    Complex Numbers
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    Problem Bank - Complex Numbers

    Access custom-built, exam-style problems for complex numbers. Each problem has a full solution and mark-scheme, as well as AI grading and support.

    39 Problems Available

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    IB: 4
    1

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    0 / 6

    Consider the equation z2+(2+2i)z+10i−15=0, where z∈C.

    1. Write down

      1. the sum of the roots.

        [1]
      2. the product of the roots.

        [1]

    It is given that z2+(2+2i)z+10i−15=0 has a real root.

    1. Find both roots of the equation.

      [4]
    2

    !

    0 / 5

    Consider the equation 5−z−3z∗​=2i, where z=a+bi and a,b∈R.

    Find the values of a and b.

    [5]
    3

    !

    0 / 5

    Consider the complex numbers w=3−4i and z=a−2ai, where a>0.


    It is given that ∣wzw∗∣=5.

    1. Show that ∣z∣=51​.

      [3]
    2. Hence find the value of a.

      [2]
    4

    !

    0 / 4

    Find all the solutions z∈C to the equation z+z2​=1.

    [4]
    5
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    0 / 4

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