Complex plane

The complex plane is a way to represent complex numbers visually. Each complex number $z = a + bi$ can be shown as a point on a plane, where $a$ is the horizontal (real) part and $b$ is the vertical (imaginary) part.

Important properties

• The horizontal axis is called the real axis.

• The vertical axis is called the imaginary axis.

• The point $(a, b)$ on the plane represents the complex number $a + bi$.

• The distance from the origin to the point $(a, b)$ is $|z| = \\sqrt{a^2 + b^2}$, called the modulus.

• The angle from the positive real axis to the line joining the origin to $(a, b)$ is called the argument of $z$.