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Math Help - a + bi form

  1. #1
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    a + bi form

    Put into a + bi form.

    i^102= ?


    i^1802= ?
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  2. #2
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    Quote Originally Posted by tmac11522 View Post
    Put into a + bi form.

    i^102= ?


    i^1802= ?
    i^{102} = i^{100} i^2 = (i^{4})^{25} i^2 = \, ....

    Use the same idea with the second one.
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  3. #3
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    i^1 = i
    i^2 = -1
    i^3 = -i
    i^4 = 1

    the pattern repeats as you continue with higher powers of i

    i^{102} = (i^2)^{51} = (-1)^{51} = -1

    or ...

    i^{102} = i^{100} \cdot i^2 = (i^4)^{25} \cdot (-1) = 1^{25} \cdot (-1) = -1

    so ... i^{102} is a real number (imaginary part is zero).


    you try it with i^{1802}
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