Complex plane
![Geometric representation of z and its conjugate z̅ in the complex plane. The distance along the light blue line from the origin to the point z is the modulus or absolute value of z. The angle ψ is the argument of z.](/Images/godic/202501/05/Complex_conjugate_picture.svg4845.png")
![Riemann sphere which maps all but one point on a sphere to all points on the complex plane](/Images/godic/202501/05/Stereographic_projection_in_3D4845.png")
![Mandelbrot fractal, imagined on a complex plane](/Images/godic/202501/05/Mandelset_hires4845.png")
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the orthogonal 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.