If z + 1 z + 1 = 0 , then z 2003 + 1 z 2003 is equal to

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Question: Answered & Verified by Expert

If

z + \frac{1}{z} + 1 = 0,

then

z^{2003} + \frac{1}{z^{2003}}

is equal to

MathematicsComplex NumberJEE Main

Options:

A $1$
B $- 1$
C $0$
D None of these

Solution:

1486 Upvotes Verified Answer

The correct answer is:

- 1

Given equation can be written as

z^{2} + z + 1 = 0

\Rightarrow

z = ω, ω^{2} (roots)

Now,

z^{2003} = ω^{2003} = ω^{2}

z^{2003} + \frac{1}{z^{2003}} = ω^{2} + \frac{1}{ω^{2}} = ω^{2} + ω = - 1

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