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Powers of (1 + i) and (1 - i) using (1 + i)^2 = 2i

This type of question, asked 3 times: 19 Apr 2026 S1, 12 May 2026 S1, 15 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    19 Apr 2026 S1

    52
    The smallest positive integer nn for which (1+i)n(1−i)n−2\dfrac{(1 + i)^n}{(1 - i)^{n-2}} is a real number, is ...

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  2. Question 2

    12 May 2026 S1

    56
    If n∈Zn \in Z, then the expression 2n(1−i)2n+(1+i)2n2n\dfrac{2^n}{(1 - i)^{2n}} + \dfrac{(1 + i)^{2n}}{2^n} is equal to ...

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  3. Question 3

    15 May 2026 S1

    54
    If n∈Zn \in Z, then the value of 2n(1+i)2n+2n(1−i)2n+(1+i)2n+(1−i)2n2n\dfrac{2^n}{(1+i)^{2n}} + \dfrac{2^n}{(1-i)^{2n}} + \dfrac{(1+i)^{2n} + (1-i)^{2n}}{2^n} is equal to

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