JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Hard

1 of 1

Application +4 | -1

z

is a complex number satisfying

z + {z^{ - 1}} = 1,

then

{z^n} + {z^{ - n}},n \in N

has the value

View answer and explanation

Correct option: A

2{\left( { - 1} \right)^n},

when

n

is a multiple of 3

Option A (

2{\left( { - 1} \right)^n},

when

n

is a multiple of 3) is correct because solving the given equation yields

z = -\omega

z = -\omega^2

, and substituting these values into

z^n + z^{-n}

gives the stated result when n is a multiple of 3.

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