page_title: Complex plane
section_title: See also
hierarchical_section_title: Complex plane / See also
caption_attribution_description: English: Hi-resolution Mandelbrot set with axes
context_page_description: In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis. It can be thought of as a modified Cartesian plane, with the real part of a complex number represented by a displacement along the x-axis, and the imaginary part by a displacement along the y-axis.
  The concept of the complex plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors. The multiplication of two complex numbers can be expressed most easily in polar coordinates—the magnitude or modulus of the product is the product of the two absolute values, or moduli, and the angle or argument of the product is the sum of the two angles, or arguments. In particular, multiplication by a complex number of modulus 1 acts as a rotation.
  The complex plane is sometimes known as the Argand plane or Gauss plane.
context_section_description: Constellation diagram
  Riemann sphere
  s-plane
  In-phase and quadrature components
  Real line
caption: Mandelbrot fractal, imagined on a complex plane
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