In mathematics, a complex plane is a geometric representation of a complex number established by a horizontal real axis and a vertical imaginary axis. With regard to a real plane with a specific algebraic structure, the real part of a complex number is represented by the displacement along the X axis, and the imaginary part is represented by the displacement along the Y axis. Under addition, the length or module length of the product is the product of two absolute values or module lengths.

The angle or angular spread of the product is the sum of two angles or angular spreads. On the complex plane, the angle between the vector corresponding to a complex number and the positive direction of the X axis is called the angle of the complex number. Obviously, a complex number has an infinite number of angles, but only one angle in the interval (-π, π), and because a complex number can be uniquely determined by the ordered real number pair, the ordered real number pair corresponds to the points in the plane rectangular coordinate system one by one.

So complex numbers can be represented by points with coordinates. When the imaginary part is not zero, the complex number of yoke means that the real part is equal and the imaginary part is opposite. If the Ruo Xu part is zero, its * * * yoke complex number is itself, and the * * * yoke complex number of the complex number Z can sometimes be expressed as Z*.

Let z 1 = a+bi and z2 = c+di be any two complex numbers. The real part of sum is the sum of the original two complex real parts, and its imaginary part is the sum of the original two imaginary parts. The sum of two complex numbers or a complex number. That is (a+bi) (c+di) = (a c)+(b d).