Trigonometry and the addition formula for cosine and sine results in \[\begin{aligned} x'&=r\cos(\theta+\psi) \\ &=r(\cos\theta\cos\psi -\sin\theta\sin\psi )\\&=x\cos\theta-y\sin\theta \\ y'&=r\sin(\t...Trigonometry and the addition formula for cosine and sine results in x′=rcos(θ+ψ)=r(cosθcosψ−sinθsinψ)=xcosθ−ysinθy′=rsin(θ+ψ)=r(sinθcosψ+cosθsinψ)=xsinθ+ycosθ. Writing the equations for x′ and y′ in matrix form, we have \[\left(x′y′\right)=\left(\begin{array}{rr}\cos\theta&-\sin\theta \\ \sin\theta&\cos\theta\…
This page reviews the arithmetic of complex numbers, introducing the imaginary unit i and defining complex numbers as a+bi. It covers operations such as addition, multiplication, and complex...This page reviews the arithmetic of complex numbers, introducing the imaginary unit i and defining complex numbers as a+bi. It covers operations such as addition, multiplication, and complex conjugation. The Fundamental Theorem of Algebra is discussed, stating that every polynomial of degree n has n complex roots, including complex conjugates. Examples are provided to demonstrate how to find these complex roots.