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Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberMiscellaneous/MixedMedium2 minQB

MathematicsMediumnumerical

If $z_{1}, z_{2}, z_{3} \in C$ satisfy $∣ z_{1} ∣ = ∣ z_{2} ∣ = ∣ z_{3} ∣ = 1, z_{1} + z_{2} + z_{3} = 1, z_{1} z_{2} z_{3} = 1$ , and $Im z_{1} < Im z_{2} < Im z_{3}$ , find

Answer:

2.00

Solution:

The numbers are roots of z^3-z^2+z-1=0, hence -i,1,i in order. Then (-i)^2017+1^2018+i^2019=2.

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

⏱ 2mℹ️ Source: QB

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