Complex plane facts for kids
The complex plane is a special kind of graph that helps us understand complex numbers. Think of it like a regular graph with an X and Y axis, but here, the horizontal line is called the real axis, and the vertical line is called the imaginary axis.
Every complex number can be written in the form a+bi. Here, a and b are just regular real numbers, and i is a special number that is the square root of -1. To find a+bi on the complex plane, you move a steps along the real axis and b steps along the imaginary axis.
You can also describe points on the complex plane using polar coordinates. This means you use the length of a line from the center to the point, and an angle that shows its direction.
The complex plane is useful for drawing graphs of special math problems called complex functions. These functions help scientists and engineers study many things, like how cars and airplanes move, how atoms work, and how electricity flows.
What are complex conjugates?
Every complex number, like z=a+bi, has something called a complex conjugate. It's written as 
. The conjugate of a+bi is a-bi.
On the complex plane, a complex number and its conjugate are like mirror images of each other. The "mirror" is the real axis. So, if you fold the paper along the real axis, the number and its conjugate would land on top of each other.
Images for kids
-
This shows how a complex number z = x + yi looks on the complex plane. The distance from the center to the point is called the modulus or absolute value. The angle θ is called the argument.
Related pages
See also
In Spanish: Plano complejo para niños
