Argand diagram
An Argand diagram is simply a picture of complex numbers drawn on the complex plane. The two terms are nearly interchangeable; “complex plane” names the abstract space, while “Argand diagram” usually names a concrete drawing of particular numbers, vectors, or shapes on it. It is named after Jean-Robert Argand, who popularized the geometric representation in 1806.
On the diagram, each complex number a + bi appears as a point at (a, b), and it is often drawn as an arrow from the origin to that point. Drawing the arrow makes the geometry vivid: its length is the modulus and the angle it makes with the positive real axis is the argument.
Argand diagrams are a thinking tool, not a separate theory. They let you see at a glance things like which numbers have the same distance from the origin (a circle), or how multiplying by i rotates a point a quarter turn counterclockwise.
On an Argand diagram, the four numbers 1, i, -1, -i form a square around the origin, each at distance 1.
Equal-modulus numbers lie on a circle centered at the origin.