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de Moivre's theorem gives us that (cos(x) + i sin(x))ⁿ = cos(nx) + i sin(nx), for integers n and real values x.Therefore cos(5x) + i sin(5x) = (cos(x) + i sin(x))⁵ = cos⁵(...

State de Moivre's theorem. Use n =5 and solve. I'll show this on the whiteboard.

Here we use the complex exponential form of 1 which is e^(i 2n pi). Applying the sixth root and substituting in for integer values of n gives all roots in complex exponential form.These can be converted i...

The simplest way to describe a complex number is by its real and imaginary part, z=x+yi, this may be wrote as Re(z)=x and Im(z)=y. These complex numbers follow the same r...

First we remember that sinθ can be expressed in terms of powers of z, where z=cos(θ)+isin(θ), using the following:2isin(nθ)=zⁿ-z⁻ⁿ and 2cos(nθ)=zⁿ+z⁻ⁿ
so, [2isin(θ)]⁴=[z¹-z⁻¹]⁴ 16sin(θ)=(z)⁴(-z⁻¹)⁰+4...