It is an easy task taking the square root of a positive number; however taking the square root of a negative number requires the use of imaginary number. The imaginary number, i is equal to the square root of negative 1 or -1^(1/2). Through the use of imaginary numbers, it had been possible to get the square root of a negative number simply by taking the square root of the number without the negative sign and multiplied by the letter i or simply the square root of -1.
Thus, we can write the square root of -4 as 2i since the square root of 4 is 2 and the square root of -1 is i. The product of a real number with an imaginary number also resulted in an imaginary number. We can also take the sum and difference of imaginary numbers by following the same rule that governs the addition and subtraction of integers. Thus, i+i=2i and – i+(-i)=-2i. Also, 2i-i=i and -2i-i=-3i. We can also add an imaginary number with a real number and result is called complex numbers.
By adding 3 to 2i the result will be 3+2i where 3 is the real number. In general, complex numbers have the form a+bi where a is the real component and b is the imaginary component. In taking the value i that is raised to the nth power, a general rule can also be followed. i raise to 0 is equal to 1 and since i squared is equal to the square root of -1 quantity squared, i squared is equal to -1. Also i raise to 3 is equal to –i since it is equal to -1*i and i raise to 4 is equal to i squared times i squared is equal to 1.
By increasing the exponent by 1 you will arrive at the same values i. e. i, -1, -i and 1 repeatedly. To simplify the results, a major pattern can be used. To find the value of i that is raise to any power, the first thing to do is to divide the exponent by 4. The remainder will determine the value; if the remainder is 0 then the value is 1, if 1 then i, if 2 then -1 and if 3 then –i. Now the question is what is the significance of imaginary number? Can it be used in real life situations and who does use it?
Imaginary numbers is applicable in several fields. One of the most important applications of imaginary numbers in real life is that imaginary numbers are often used in studying some physical phenomena such as in making a model of flow of flow of fluid that passes through various obstacles, for example a round pipe. Through the use of imaginary or complex numbers, the problem that one may face is greatly lessened. One of the fields wherein imaginary and complex numbers play an important role is the field of electrical engineering.
Imaginary numbers or complex numbers are being use by electrical engineers to make amplitude and segment or phase of an electrical swinging and alternation be in track such as electrical voltage and current that power electrical appliances. Also, in quadratic equations in electrical circuits, imaginary and complex numbers are used by electrical engineers wherein the behavior of the given circuit depends on whether the value of the root is real or imaginary. For electrical engineers, the uses of complex numbers are incredibly important.
In this modern time new technologies exist, cell phones is one of the modern technologies that is in demand. Imaginary numbers are being useful in the signal processing which was applied in the telecommunication process, the use of cellular phones. Navigations of the airplanes that were made possible by the radar and even the study of biology, which is in terms of analyzing firing events from the brains neurons, are some other developments made possible my imaginary numbers. In one of the fields of physics such as quantum mechanics the applications of imaginary numbers or complex numbers are being used.
Imaginary numbers in quantum mechanics is very important to form the descriptions of the electronic states in materials and this may lead to the application of optics, the fluorescent as well as the incandescent lights and some types of cameras, even the polarization descriptions for polarized sunglasses, semiconductor devices, transistors and electronics as well as magnetism, which was apply to magnetic disk drives and some other storage devices. Also in the field of chemistry in the covalent bonding between atoms is another application of imaginary numbers.
Although we may not know it but the application of imaginary numbers are too many and in almost every field of study especially in the field of mathematics and different branches of science.
Conjecture Corporation. (2008). What is an imaginary number?. Retrieved January 13, 2008 from http://www. wisegeek. com/what-is-an-imaginary-number. htm David, E, J. (1999). Complex numbers. Retrieved January 13, 2008 from http://www. clarku. edu/~djoyce/complex/plane. html Drexel University. (2008). Imaginary numbers in real life. Retrieved January 13, 2008 from Lifehttp://mathforum. org/library/drmath/view/53606. htmlSample Essay of StudyFaq.com