Complex Numbers and Quaternions

Abstract

A complex number z is a number of the form a + bi where a and b are real numbers and i 2 = − 1. Cardona, who was a sixteenth century Italian mathematician, introduced complex numbers, and he used them to solve cubic equations. The set of complex numbers is denoted by ℂ, and each complex number has two parts namely the real part Re(z) = a, and the imaginary part Im(z) = b. The set of complex numbers is a superset of the set of real numbers, and this is clear since every real number is a complex number with an imaginary part of zero. A complex number with a real part of zero (i.e. a = 0) is termed an imaginary number. Complex numbers have many applications in physics, engineering and applied mathematics.