Hyper Complex Numbers

Complex Numbers

In spite of Calvin’s discomfiture, imaginary numbers (a subset of the set of complex numbers) exist and are invaluable in mathematics, engineering, and science. In fact, in certain fields, such as electrical engineering, aeronautical engineering and quantum mechanics, progress has been critically dependent on complex numbers and their behavior. In the context of mathematical biology, a number o...

Complex Numbers

This article discusses some introductory ideas associated with complex numbers, their algebra and geometry. This includes a look at their importance in solving polynomial equations, how complex numbers add and multiply, and how they can be represented. Finally we look at the nth roots of unity, that is, the solutions of the equations z = 1. 1 The Need For Complex Numbers The shortest path betwe...

Complex Numbers and Exponentials

respectively. It is conventional to use the notation x+iy (or in electrical engineering country x+jy) to stand for the complex number (x, y). In other words, it is conventional to write x in place of (x, 0) and i in place of (0, 1). In this notation, the sum and product of two complex numbers z1 = x1 + iy1 and z2 = x2 + iy2 is given by z1 + z2 = (x1 + x2) + i(y1 + y2) z1z2 = x1x2 − y1y2 + i(x1y...

Week 4 – Complex Numbers

Cartesian and polar form of a complex number. The Argand diagram. Roots of unity. The relationship between exponential and trigonometric functions. The geometry of the Argand diagram. 1 The Need For Complex Numbers All of you will know that the two roots of the quadratic equation ax + bx+ c = 0 are x = −b± √ b2 − 4ac 2a (1) and solving quadratic equations is something that mathematicians have b...

Arithmetic With Complex Numbers