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The 48 pages that link to Complex plane, each with the reason it gives.

• Complex numberRelated: It represents each complex number as the point (a, b).

• Quadratic equationRelated: Nonreal quadratic roots appear as points reflected across the real axis.

• Complex exponentialRelated: The function maps complex inputs and outputs within this plane.

• Unit circleRelated: Its points with modulus one form the unit circle used to represent complex phases.

• PhasorRelated: A phasor’s magnitude and phase correspond to polar coordinates in this plane.

• Entire functionRelated: Entire functions must be holomorphic at every point of this domain.

• Riemann mapping theoremRelated: It is the ambient space in which the theorem's domains lie.

• Polar coordinate systemRelated: A complex number can also be written using polar radius and argument.

• Cauchy–Riemann equationsRelated: Its two coordinate directions produce the paired partial derivatives in the equations.

• Complex conjugateRelated: Conjugation is reflection across this plane’s real axis.

• Contour integrationRelated: Contours are oriented curves drawn in this plane.

• Imaginary unitRelated: It gives i the geometric position one unit above the origin.

• Similarity transformationRelated: Multiplication by a nonzero complex number expresses planar scaling and rotation compactly.

• Euler's identityRelated: It makes the rotation encoded by the exponent visible as a point on the plane.

• Nyquist stability criterionRelated: Nyquist contours and their critical point are interpreted in this plane.

• Circle packingRelated: Complex coordinates make conformal maps and circle configurations easier to describe.

• Mandelbrot setRelated: The set is plotted as a region in this plane of possible parameters.

• Stereographic projectionRelated: Stereographic projection supplies planar coordinates for points on the Riemann sphere.

• Complex derivativeRelated: It supplies the many approach directions that constrain the derivative.

• Polar formRelated: It gives geometric meaning to a complex number's distance and direction.

• Zero of a functionRelated: Complex zeros need not appear as intersections with the real graph’s horizontal axis.

• Magnitude (mathematics)Related: Magnitude appears geometrically as radial distance from the plane’s origin.

• Napoleon's theoremRelated: Complex coordinates encode the side rotations and make the center-distance equality tractable.

• Imaginary numberRelated: Imaginary numbers lie along its vertical axis.

• Clifford's circle theoremsRelated: Complex coordinates encode circles and their intersections in compact algebraic form.

• Gershgorin circle theoremRelated: Each row of a matrix defines a disk in this plane.

• Lester's theoremRelated: Complex coordinates offer another way to express triangle vertices and test circle membership.

• Pompeiu's theoremRelated: Complex coordinates offer an algebraic way to represent the triangle's vertices and compare distances.

• Rotations in 4-dimensional Euclidean spaceRelated: Each invariant rotation plane can be modeled as a complex line.

• Thébault's theoremRelated: Complex multiplication compactly represents the quarter-turns used to locate the square centers.

• Two-dimensional spaceRelated: It gives two-dimensional coordinates an algebraic interpretation.