Argand

Argand may refer to the Argand diagram or to Jean-Robert Argand, a mathematician associated with the geometric interpretation of complex numbers.

Jean-Robert Argand was a Swiss-born mathematician active in the late 18th and early 19th centuries. He is credited with introducing a geometric representation of complex numbers by placing them as points in a two-dimensional plane, now known as the Argand diagram. This view treats each complex number z = a + bi as the point (a, b) in the plane, with the real part a on the horizontal axis and the imaginary part b on the vertical axis. Argand’s construction laid groundwork for the modern treatment of complex numbers as objects that can be added, multiplied, and analyzed using geometric intuition.

The Argand diagram, or complex plane, provides a visual framework for complex arithmetic. In this plane, the modulus of z is the distance from the origin to the point, and the argument is the angle formed with the positive real axis. Addition corresponds to vector addition, while multiplication combines rotation by the arguments and scaling by the moduli. Expressing a complex number in polar form, z = r(cos θ + i sin θ), emphasizes these geometric interpretations. The diagram also aids in understanding roots, power, and mapping properties of complex functions.

Today, the Argand diagram is a standard tool in complex analysis, engineering, and physics, offering a clear, intuitive way to visualize complex numbers and their operations. The term Argand may also be encountered as a surname associated with the historical development of complex number geometry.