We can represent complex numbers graphically on a x–y coordinate system where point (a, b) represents the complex number a+bi. We call this the rectangular form of complex numbers.

We will write the set of all real numbers as R and the set of all complex numbers as C. Often the letters z, w, v, and s, and r are used to denote complex numbers.

In this section we show how to add and subtract complex numbers, and how to multiply a complex number by a scalar (i.e. a real number) using the common operations of addition, subtraction, and …

A complex number z = a + b^{ can be graphed by plotting the number in the plane using the x-axis as the real axis and the y-axis as the imaginary axis and plotting z at the location (a; b).

3.1 Graphical Representation of Complex Numbers As you learned in high-school algebra, any ordered pair of numbers can be located on a two-dimensional (2-D) graph, e.g., using the Cartesian …

1.1 Algebra of Complex Numbers The number i is declared by law to satisfy the equation i2 = −1. A complex number is an expression of the form x + yi, with x and y real numbers. Complex numbers …

Any complex number z can be written as the sum of a real part and an imaginary part: z = [Re z] + i[Im z] ; where the numbers or variables in the []'s are real. So z = x + y i with x and y real is in this form …