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}

1. Complex Variables Formulas

• 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.

  Related Documents

  • Mathematical Formula Handbook

• 1.1 De Moivre's Theorem

  Equation

  
  
  

  Latex Code

              (\cos \theta + i \sin \theta)^{n}=e^{in\theta}=\cos n\theta + i \sin n\theta
          

  Explanation

  • : The power n of equals to

  Related Documents

  • Mathematical Formula Handbook

• 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

  Related Documents

  • Mathematical Formula Handbook

• 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

  Related Documents

  • Mathematical Formula Handbook

• 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

  Related Documents

  • Mathematical Formula Handbook

• 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

  Related Documents

  • Mathematical Formula Handbook

• 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

  • : The ln(1+z) equals to summation of power series of

  Related Documents

  • Mathematical Formula Handbook