From the de Moivre's we have, <span> (cosθ+isinθ)^n=cos(nθ)+isin(nθ) </span><span> Therefore, </span><span> R((cosθ+isinθ)^5)=cos(5θ)I((cosθ+isinθ)^5)=sin(5θ) </span><span> Simplifying, </span><span> cos^5(θ)−10(sin^2(θ))(cos^3(θ))+5(sin^4(θ))(cosθ)=cos(5θ) </span><span> </span>