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.

A complex number z is given by a pair of real numbers x and y and is written in the form z = x+iy, where i satis es i2 = 1. The complex numbers may be represented as points in the plane, with …

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.

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 …

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 …

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, …

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).