In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal x -axis, called the real axis, is formed by the real numbers, and the vertical y -axis, called the imaginary axis, is formed by the imaginary numbers.

The complex plane is a plane with: real numbers running left-right and; imaginary numbers running up-down. To convert from Cartesian to Polar Form: r = √(x 2 + y 2) θ = tan-1 ( y / x ) To convert from Polar to Cartesian Form: x = r × cos( θ) y = r × sin(θ) Polar form r cos θ + i r sin θ is often shortened to r cis θ

A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1.

2025年1月31日 · The complex plane is the plane of complex numbers spanned by the vectors 1 and i, where i is the imaginary number. Every complex number corresponds to a unique point in the complex plane. The line in the plane with i=0 is the real line.

2023年12月13日 · Complex numbers are the points on the plane, expressed as ordered pairs \((a,b)\), where \(a\) represents the coordinate for the horizontal axis and \(b\) represents the coordinate for the vertical axis.

2024年12月3日 · The complex plane, also known as the Argand plane, provides a geometric framework for visualizing complex numbers. It consists of two perpendicular axes: the horizontal axis represents the real part of a complex number, …

numbers can be visualized as points in a plane: plot x+ yiat the point (x;y). Addition and subtraction of complex numbers has the same geometric interpretation as for vectors.

Complex numbers are an extension of the real number system with useful properties that model two-dimensional space and trigonometry. A complex number is written as (3+ 2i) and is visualized as a point in the complex plane with the horizontal component of 3 and a vertical component of 2.

The complex plane (also known as the Gauss plane or Argand plane) is a geometric method of depicting complex numbers in a complex projective plane. It is usually a modified version of the Cartesian plane, with the real part of a complex number denoted by a displacement along the x-axis, and the imaginary part by a displacement along the y-axis.

A complex number z is given by a pair of real numbers x and y and is written in the form z = x+iy, where i satis es i2 = 1. The complex numbers may be represented as points in the plane, with the real number 1 represented by the point (1; 0), and the complex number i …