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 number, i.e., …

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, including in number …

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 and subtract with …

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 axis and the …

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