If i=sqr-1, what is the value of i^3? -1 i 1 -i

Question

If i=sqr-1, what is the value of i^3?
-1
i
1
-i

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Lệ Thu 3 years 2021-08-27T08:51:21+00:00 1 Answers 8 views 0

Answers ( )

  1. huyenthanh
    0
    2021-08-27T08:52:37+00:00
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    Answer:

    After solving we get \mathbf{i^3=-i}

    Option D is correct.

    Step-by-step explanation:

    We are given:

    If  i=\sqrt{-1} we need to find the value of i^3

    Solving:

    i=\sqrt{-1}

    Taking cube on both sides

    i^3=(\sqrt{-1})^3\\

    We can write a^3= a^2.a^1 Using this for solving:

    i^3=(\sqrt{-1})^2.(\sqrt{-1})\\We \ know \ (\sqrt{-1})^2 =- 1 \ and \ \sqrt{-1}=1 \\i^3=-1(i)\\i^3=-i

    So, after solving we get \mathbf{i^3=-i}

    Option D is correct.

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