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Re

Denotes the real part of a complex number in mathematical notation.

Overview

Essential in complex analysis and related mathematical fields where separating real and imaginary components is necessary.

  • Commonly used in electrical engineering when analyzing circuits with complex impedances
  • Appears frequently in signal processing and Fourier analysis
  • Often paired with Im for complete complex number representation
  • Standard notation in physics when dealing with wave functions and quantum mechanics

Examples

Expressing the real part of a complex number z.

ℜ(z)=x where z=x+iy\Re(z) = x \text{ where } z = x + iy 
\Re(z) = x \text{ where } z = x + iy

Writing the real part of a complex exponential function.

ℜ(eiθ)=cos⁡(θ)\Re(e^{i\theta}) = \cos(\theta) 
\Re(e^{i\theta}) = \cos(\theta)

Showing the real component in a complex integral solution.

ℜ(∮Cdzz)=2πi\Re\left(\oint_C \frac{dz}{z}\right) = 2\pi i 
\Re\left(\oint_C \frac{dz}{z}\right) = 2\pi i