Class 11Mathematics1 Complex Numbers and Quadratic Equations: Complex NumbersDe Moivre's theorem and Roots of unity
DifficultIf $z^2+z+1=0$,where $z$ is a complex number,then $\left(z+\frac{1}{z}\right)^3+\left(z^4+\frac{1}{z^4}\right)^3$ is equal to
- A$1$
- B$0$
- C-$1$
- D-$2$
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If $\alpha, \beta$ are the roots of the equation $x^2+x+1=0$,then $(\alpha+\beta)^2+(\alpha^2+\beta^2)^2+(\alpha^3+\beta^3)^2+\ldots+(\alpha^{12}+\beta^{12})^2=$
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If $n$ is a positive integer, then $(1 + i\sqrt{3})^{2n} + (1 - i\sqrt{3})^{2n}$ is equal to .........
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