If z + z 1 = 1 , find z 99 + z 99 1 .

Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberMiscellaneous/MixedMedium2 minQB

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If $z + \frac{1}{z} = 1$ , find $z^{99} + \frac{1}{z ^{99}}$ .

Answer:

Solution:

z^2-z+1=0, so z is -omega or -omega^2. In either case z^99=-1, hence the sum is -2.

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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