Origin Of Complex Numbers

Introduction to origin of complex numbers:

Definition of a complex number:

A complex number is a kind of number which consists of a real value and imaginary value.The complex value is represented in the form of a+ib. In this a and b represents the real value and i represents an imaginary value.And here the value for i2 is -1. The square value of an imaginary number is a real number. In this article we will discuss about the origin of complex numbers.

Origin of Complex Numbers:

The first reference for the origin of complex numbers is got by cardan at 1545.when cardan finding the roots of polynomial he found the complex numbers.During this time period the notation sqrt(-1) was used. When we put the polynomials in to the categories this sqrt(-1) was used as a very important notation.but it was not used as a real mathematical object.

During the time period of 1777, Euler solved some of the problems using the i and i notation for the two different square roots of -1.

During the time period of 1797 wessel used the complex numbers geometric interpretation points in a plane and in the year of 1799 guass also used the complex numbers geometric interpretation points in a plane. This made the complex numbers somewhat real and less strange.

Finally, during the year of 1833 Hamilton showed the pairs of real numbers for this complex numbers.And Euler told that the i may be in any of this real part.

In nowadays the complex numbers are used in variety of sciences and the related fields such as signal processing, controltheory,electomagnetism,fluiddynamics,quantummechanics,cartography and vibration analysis.

Example Problem in Origin of Complex Number:

Here we will see some example problem for addition of complex numbers.

Example 1:

Add:4i+3i

Solution:

=4i+3i

=7i

Example 2:

Add:(4+3i)+(2+5i)

Solution:

=(4+3i)+(2+5i)

=4+3i+2+5i

=4+2+3i+5i

=6+8i

Example 3:

subtract:4i-3i

Solution:

=4i-3i

=i

Example 4:

subtract:(4+3i)-(2+5i)

Solution:

=(4+3i)-(2+5i)

=4+3i-2-5i

=4-2+3i-5i

=2-2i

A complex number is a number that can be put in the form a + bi, where a and b are real numbers and i is called the imaginary unit, where i2 = -1.[1] In this expression, a is called the real part and b the imaginary part of the complex number. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part. The complex number a + bi can be identified with the point (a, b) in the complex plane. A complex number whose real part is zero is said to be purely imaginary, whereas a complex number whose imaginary part is zero is a real number. In this way the complex numbers contain the ordinary real numbers while extending them in order to solve problems that cannot be solved with real numbers alone.

Understand Perfect Square Formulais always challenging for me but thanks to all math websites to help me out.

Complex numbers are used in many scientific and engineering fields, including physics, chemistry, biology, economics, electrical engineering, mathematics, and statistics. The Italian mathematician Gerolamo Cardano is the first known to have introduced complex numbers. He called them "fictitious" during his attempts to find solutions to cubic equations in the 16th century,[2] but complex numbers are no more or less "fictitious" or "imaginary" than any other kind of number.

by: johnharmer

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