Complex Numbers
Tags: #math #complex numbersEquation
$$z=x+iy=r(\cos \theta + i \sin \theta)=re^{i(\theta+2n\pi)} \\ z^{*}=x-iy=r(\cos \theta - i \sin \theta)=re^{-i\theta} \\ zz^{*}=|z|^{2}=x^{2}+y^{2}$$Latex Code
z=x+iy=r(\cos \theta + i \sin \theta)=re^{i(\theta+2n\pi)} \\
z^{*}=x-iy=r(\cos \theta - i \sin \theta)=re^{-i\theta} \\
zz^{*}=|z|^{2}=x^{2}+y^{2}
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Introduction
Latex Code
z=x+iy=r(\cos \theta + i \sin \theta)=re^{i(\theta+2n\pi)} \\
z^{*}=x-iy=r(\cos \theta - i \sin \theta)=re^{-i\theta} \\
zz^{*}=|z|^{2}=x^{2}+y^{2}
Explanation
: i denotes the complex component of a complex number.
: The real quantity r is the modulus of z.
: The angle \theta is the argument of z.
: The complex conjugate of z.
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