Multiple Choice Questions on The value of i radic 3 2 40 i radic 3 2 4 is ........ for NDA Exam Preparation

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Multiple Choice Questions

The value of i radic 3 2 40 i radic 3 2 4 is ........

Mathematics (NDA) Complex Numbers
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    The value of {(i + √3)/2}40+ {(i -√3)/2}4 is ?

    -1

    Correct Answer

    1

    Incorrect Answer

    2

    Incorrect Answer

    -2

    Incorrect Answer
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    Explanation:

    ( i +√3)/2 = i (i +√3)/2i

    =( i2 + i√3)/2i

    = (-1 + √3i)/2i

    = ω/i ( i -√3)/2

    = i (i -√3)/2i

    = (-1 -√3i)/2i

    = ω2 /i

    Therefore , {( i+√3)/2}40+ {(i-√3)/2}40

    = (ω/i)40+ (ω2 /i)40

    = ω40 /i40 + ω80/i40

    = ω + ω2 ( since i4 = 1)

     = -1 ( since 1 +ω +ω2 =0)

    By: bhavesh kumar singh
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