Multiple Choice Question (MCQ)

If i=\sqrt{-1} , for which of the following values of n does i^n+(-i)^n have a positive values?

  1. ×

    23

  2. 24

  3. ×

    25

  4. ×

    26

  5. ×

    27

Collected in the board: Imaginary number

Steven Zheng posted 2 months ago


Answer

  1. Raising the powers of i, a pattern develops.

    i^1 = i

    i^2 = -1

    i^3= -i

    i^4= 1

    i^5= i

    Raising the powers of -i, another pattern develops.

    (-i)^1 = -i

    (-i)^2 =-1

    (-i)^3 = i

    (-i)^4 = 1

    (-i)^5 = -i

    So when the powers of i and -i is multiples of 4, their exponents are both equal to 1. That is,

    When n=24 , i^n+(-i)^n=1=1=2

Steven Zheng posted 2 months ago

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