Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberMiscellaneous/MixedMedium2 minQB

MathematicsMediumsingle choice

Find $\sum_{k = 1}^{100} (i^{k!} + ω^{k!})$ , where $i = - 1$ and $ω$ is a non-real cube root of unity.

Answer:

Solution:

For k>=4, i^(k!)=1, giving sum i^(k!)=95+i. For k>=3, omega^(k!)=1, giving 97. Total=192+i.

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

⏱ 2mℹ️ Source: QB

Loading discussions...