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Modulus of a product or quotient of complex numbers

This type of question, asked 2 times: May 2021 S1, 16 Apr 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    May 2021 S1

    144
    If z=(3+i)3(3i+4)2(8+6i)2z = \dfrac{(\sqrt{3}+i)^3(3i+4)^2}{(8+6i)^2}, then ∣z∣|z| is equal to

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  2. Question 2

    16 Apr 2026 S1

    52
    If (1+i)⋅(1+2i)………(1+ni)=x+iy(1 + i)\cdot(1 + 2i)\ldots\ldots\ldots(1 + ni) = x + iy (Where i=−1i = \sqrt{-1} ), then the value of (2)⋅(5)⋅(10)………(1+n2)(2)\cdot(5)\cdot(10)\ldots\ldots\ldots(1 + n^2)

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