Class 11Mathematics1 Complex Numbers and Quadratic Equations: Complex NumbersDe Moivre's theorem and Roots of unity
MediumThe real part of $z$ that satisfies $i z^4+1=0$ is
- A$\sin \frac{\pi}{4}$
- B$\cos \frac{\pi}{8}$
- C$0$
- D$-1$
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Similar Questions
If $\theta = \frac{\pi}{6}$,then the $10^{th}$ term of the series $1 + (\cos \theta + i \sin \theta) + (\cos \theta + i \sin \theta)^2 + (\cos \theta + i \sin \theta)^3 + \ldots$ is equal to:
DifficultAP EAMCET 2001
View SolutionCommon roots of the equations $z^3 + 2z^2 + 2z + 1 = 0$ and $z^{1985} + z^{100} + 1 = 0$ are
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View SolutionThe product of the distinct $(2n)^{\text{th}}$ roots of $1+i\sqrt{3}$ is equal to:
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View SolutionIf $y = \cos \theta + i\sin \theta$,then the value of $y + \frac{1}{y}$ is
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View SolutionTwo values of $(-8-8 \sqrt{3} i)^{1/4}$ are
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