What is the complex plane?
- The complex plane, sometimes also known as the Argand plane, is a two-dimensional plane on which complex numbers can be represented geometrically
- It is similar to a two-dimensional Cartesian coordinate grid
- The x-axis is known as the real axis (Re)
- The y-axis is known as the imaginary axis (Im)
- The complex plane emphasises the fact that a complex number is two dimensional
- i.e it has two parts, a real and imaginary part
- Whereas a real number only has one dimension represented on a number line (the x-axis only)
What is an Argand diagram?
- An Argand diagram is a geometrical representation of complex numbers on a complex plane
- A complex number can be represented as either a point or a vector
- The complex number x + yi is represented by the point with cartesian coordinate (x, y)
- The real part is represented by the point on the real (x-) axis
- The imaginary part is represented by the point on the imaginary (y-) axis
- Complex numbers are often represented as vectors
- A line segment is drawn from the origin to the cartesian coordinate point
- An arrow is added in the direction away from the origin
- This allows for geometrical representations of complex numbers
Plot the complex numbers z1 = 2 + 2i and z2 = 3 – 4i as points on an Argand diagram.
Write down the complex numbers represented by the points A and B on the Argand diagram below.