Imaginary numbers can also be applied to signal processing, which is useful in cellular technology and wireless technologies, as well as radar and even biology (brain waves). Using imaginary currents and real numbersВ helps those working with AC electricity do the calculations and avoid electrocution. Combining AC currents can be very difficult because they may not match properly on the waves. AC electricity changes between positive and negative in a sine wave. Imaginary numbers are particularly applicable in electricity, specifically alternating current (AC) electronics. Usually denoted by the symbol i, imaginary numbers are denoted by the symbol jВ in electronics (because iВ already denotes 'current'). Imaginary numbers become particularly useful in advanced calculus. In quadratic planes, imaginary numbers show up in equations that donвЂ™t touch the x axis. Imaginary numbers, also called complex numbers, are used in real-life applications, such as electricity, as well as quadratic equations. While it is not a real number - that is, it cannot be quantified on the number line - imaginary numbers are 'real' in the sense that they exist and are used in math. Essentially, an imaginary number is the square root of a negative number and does not have a tangible value.

The number i is just as normal as other numbers but the name вЂњimaginaryвЂќ stuck for purely historical reasons and the terms вЂњrealвЂќ and вЂњimaginaryвЂќ are just labels.An imaginary number is a number that, when squared, has a negative result. I dislike the term вЂњimaginary numberвЂќ it was introduced when i was discovered around 1545 by the first group of scientists who thought they were nonsense and absurd. If i exists then Maths becomes easier and new relationships emerge that are easily described. Let us assume the imaginary number i exists, whereДЄs i is just a number (like e and ПЂ) it is written in upright roman text. We can solve for x for equations such as x 2 = 25 easily, but what does the solution for x 2 = -25 mean? Although they may appear strange to us, they are no more strange than zero, negative, fractional and irrational numbers (which canвЂ™t be written as a simple fraction) appeared to scientists before us when they were first introduced. Imaginary numbers have a similar history to negative numbers, in that people didnвЂ™t or still donвЂ™t think they are вЂњrealвЂќ (pun intended). Negative numbers were not understood and were considered absurd by many great Mathematicians until the 1700s then they only came into normal usage driven partly by their short elegant way of summarizing things from book keeping to Chemical Analysis.

You shouldnвЂ™t be too smug about the use of negative numbers (donвЂ™t say вЂњI know all this, so why botherвЂќ, well be patient). A better, and more elegant way of handling the situation is to use positive and negative numbers and Maths which keep track of the direction along the number line automatically my money = -ВЈ1000 +ВЈ50 = -ВЈ950. Multiplying x by -1 вЂњflipsвЂќ you along the number line to -x.ДЇor example in words, вЂњI owe the bank ВЈ1000 and after doing some evening work I earn ВЈ50 and then pay the bank ВЈ50, then I now owe the bank ВЈ950вЂќ.

Negative numbers give you a вЂњmirror imageвЂќ of the positive number on the other side of zero on the number line, thus positive and negative numbers are all one-dimensional. I want to start by comparing imaginary numbers with their close neighbours, the negative numbers. I want to show you why they are so useful, they cut down the use of a calculator and reduce the use of trig relationships. Here giving a longer than normal introduction to imaginary and complex numbers because as a student I couldnвЂ™t see why some lecturers and professors wanted to use complex numbers instead of tangents, sines and cosines which I knew from school and also because the explanations in Maths books are not always very helpful.

Imaginary i number