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).

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, …

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.

This rst chapter introduces the complex numbers and begins to develop results on the basic elementary functions of calculus, rst dened for real arguments, and then extended to functions …

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 begin with the description of complex numbers and their basic algebraic properties. We will assume that the reader had some previous encounters with the complex numbers and will be …

We can thus represent a complex number z1 in terms of a real and imaginary component (rectangular coordinates), or in terms of a mag-nitude, jz1j, and a phase angle \z1 (polar …