List of Complex Variables Formulas Latex Code
rockingdingo 2023-03-12 #Complex Variables #Conjugate #Power Series
List of Complex Variables Formulas Latex Code
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In this blog, we will summarize the latex code for complex variables formulas, including complex numbers, De Moivreâ??s theorem and power series for complex variables e^{z}, sin(z), cos(z), ln(1+z), (1+z)^{n}, etc.
- 1. Complex Variables Formulas
- 1.0 Complex Numbers
- 1.1 De Moivre's Theorem
- 1.2 Power Series for Complex Variables e^{z}
- 1.3 Power Series for Complex Variables sin(z)
- 1.4 Power Series for Complex Variables cos(z)
- 1.5 Power Series for Complex Variables ln(1+z)
- 1.6 Power Series for Complex Variables (1+z)^{n}
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1.0 Complex Numbers
Equation
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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1.1 De Moivre's Theorem
Equation
Latex Code
(\cos \theta + i \sin \theta)^{n}=e^{in\theta}=\cos n\theta + i \sin n\thetaExplanation
: The power n of
equals to
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1.2 Power Series for Complex Variables
Equation
Latex Code
e^{z}=1+z+\frac{z^{2}}{2!}+\frac{z^{3}}{3!}+...+\frac{z^{n}}{n!}+...Explanation
: The z power e equals to summation of power series of
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1.3 Power Series for Complex Variables sin(z)
Equation
Latex Code
\sin z=z-\frac{z^{3}}{3!}+\frac{z^{5}}{5!}-...Explanation
: The sin(z) equals to summation of power series of
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1.4 Power Series for Complex Variables cos(z)
Equation
Latex Code
\cos z=1-\frac{z^{2}}{2!}+\frac{z^{4}}{4!}-...Explanation
: The cos(z) equals to summation of power series of
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1.5 Power Series for Complex Variables ln(1+z)
Equation
Latex Code
\ln (1+z)=1-\frac{z^{2}}{2!}+\frac{z^{3}}{3!}-...Explanation
: The ln(1+z) equals to summation of power series of
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1.6 Power Series for Complex Variables (1+z)^{n}
Equation
Latex Code
(1+z)^{n}=1+nz+\frac{n(n-1)}{2!}z^{2}+\frac{n(n-1)(n-2)}{3!}z^{3}+...Explanation
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