De Moivre's Theorem
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- A common situation in algebra is when we have to find the expansion of a complex number, i.e. (rcisθ)n(r\operatorname{cis}\theta)^n(rcisθ)n (where cisθ=cosθ+isinθ\operatorna…
By Rajiv Movva, Soumabho Dey, Caroline K, Anusha Rahman
- De Moivre's Theorem, named after the French statistician Abraham de Moivre, is simple enough to state, but the power of the formula lies in its ability to convert complex number…
By Wayne Zhao, Alex Federspiel
- De Moivre's Formula Using this formula, we can connect trigonometry with complex numbers. Instead of multiplying a complex number by itself over and over, the theorem provides a…
By Anusha Rahman
- (Video) De Moivre's Theorem by Anusha Rahman In this video by Anusha Rahman, you will learn about De Moivre's Theorem.
By Anusha Rahman
Problems 7
- Compute (1+i)18(1+i)^{18}(1+i)18
- If zzz is a complex number such that z=cis(θ)z = \text{cis}(\theta)z=cis(θ) for some angle θ\thetaθ and z+z−1=3,z + z^{-1} = \sqrt{3},z+z−1=3, what is the value of z2010+z−2010…
- Solve: 2 cis(π3)⋅3 cis(2π3)2 \text{ cis}\big(\frac{\pi}{3}\big) \cdot 3 \text{ cis}\big(\frac{2\pi}{3}\big)2 cis(3π)⋅3 cis(32π) (Note: cis(x)=cos(x)+isin(x)\text{cis}(x) = \…
- Find yzyzyz if y=4eπi4y = 4 e^{\frac{\pi i}{4}}y=4e4πi z=3e2πi3z = 3e^{\frac{2\pi i}{3}}z=3e32πi
- If z=reiθz = re^{i\theta}z=reiθ, then what is z2z^2z2?
- If z=−12+32iz=-\frac{1}{2}+\frac{\sqrt{3}}{2}iz=−21+23i, then what is the value of z6−1z^6-1z6−1?
- The Chebyshev polynomials of the first kind are a class of polynomials denoted TnT_nTn for any nonnegative integer n.n.n. (The T is for Tchebyshev, the French way of spelling C…