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.

bers De nition 2.1. A complex number z is a a number of the form z = a . ib where a; b 2 R. In this . ase we write z 2 C. The mod. is Im (z) = b 2 R: It is important to note that Im (z) is a real …

Complex analysis is a branch of mathematics that involves functions of complex numbers. It provides an extremely powerful tool with an unex-pectedly large number of applications, …

identify the real parts and imaginary parts of complex numbers, solve linear equations with complex numbers by setting the real parts and imaginary parts equal to each other, and add …

Two complex numbers a + bi and c + di are equal if a c and b d, that is, their real parts are equal and their imaginary parts are equal. In the Argand plane the horizontal axis is called the real …

1. Complex numbers Complex numbers are of the form z = x + iy 2 x , y R, i = −1. In the above definition,