# VCE Specialist Mathematics/Units 3 and 4: Specialist Mathematics/Relations and Regions in the Complex Plane

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## Preface[edit]

**Formal Definition:** In mathematics, the complex plane, z-plane, Argand diagrams are 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.

**Translation:** All complex numbers are vectors, they have direction, magnitude, and can be displayed using Cartesian-like coordinates on a modified Cartesian plane, or can be manipulated in polar form. Common formations are rays (angles), circles, ellipses, and other common Cartesian graphs.