Class 11Mathematics1 Complex Numbers and Quadratic Equations: Complex NumbersDe Moivre's theorem and Roots of unity
DifficultIf $x+\frac{1}{x}=2 \cos \theta$, then for any integer $n$, $x^n+\frac{1}{x^n}=$
- A$2 \cos n \theta$
- B$2 \sin n \theta$
- C$2 i \cos n \theta$
- D$2 i \sin n \theta$
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Similar Questions
The product of any two of the tenth roots of unity is
$f(x) = (\cos x + i \sin x) \cdot (\cos 3x + i \sin 3x) \cdots [\cos(2n-1)x + i \sin(2n-1)x]$,$n \in N$. Then $f''(x) = ?$ (Where $i = \sqrt{-1}$)
If $\omega$ is a cube root of unity but not equal to $1$,then the minimum value of $|a + b\omega + c\omega^2|$ (where $a, b, c$ are integers but not all equal) is
DifficultIIT 2005
View SolutionIf $x + \frac{1}{x} = 2\cos \alpha$,then $x^n + \frac{1}{x^n} = $
Easy
View SolutionIf $\alpha$ and $\beta$ are the roots of the equation $x^2 + x + 1 = 0$, then $\alpha^{2026} + \beta^{2026} = $
DifficultMHT CET 2026
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