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  • Perplex
    IB Math AAHL
    /
    Complex Numbers
    /

    Problem Bank

    [Maximum mark: 16]
    1. Using compound angle identities, show that

      (i) ​sin(125π​)=4√6+√2​​


      (ii) ​cos(125π​)=4√6−√2​​

      [6]
    2. Prove that ​sinθ−icosθ≡cisθ⋅cis(−2π​).

      [3]

    The complex number ​z​ satisfies the equation ​ze5πi/6​=41+√3​−4√3−1​i.

    1. Using parts (a) and (b), find the modulus and argument of ​z.

      [7]

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