Taking a leap of faith into imaginary numbers opens new doors in the real world through complex analysis

For a non -aqueous world, the presence of the message “I” represents a number that does not exist completely and is “fake” that can be difficult to wrap your head. If you open your mind in this way of thinking, it becomes a completely new world possible.

I Mathematics world that studies analysis: A field of mathematics that deals with it Complex numbers. Unlike the most knowledgeable real numbers – the correct positive and negative numbers, fractures, square roots, cube roots and even Numbers like PI – The complex numbers have an imaginary component. This means that it is made from both real numbers and the fictional number I: The Spring Root of negativity 1.

Remember that the sillness root of the number represents a square number is the original number. Times of the positive number itself is a positive number. The negative number times itself is a positive number. The fantasy number that showed it somehow when it doubles itself is negative.

Talks on fictional numbers with a non -water world often lead to objections such as, “but these numbers are not really present, right?” If you are one of these skeptics, you are not alone. Even sports giants found complex numbers that are difficult to swallow. For one of them, the “fictional” call does not help people understand that it is not fictional. Mathematics Girolamo CardanoIn his book 1545, which deals with complex numbers, “Ars Magna“They refused to be” hidden because they are useless. ” Leonard UrsOne of the greatest mathematicians, It is supposed to be calculated √ (-2) √ (-3) as √6. The correct answer is -6.

At high school, you may have faced the spring formula, which gives solutions to Equations in which the unknown variable is booked. Perhaps the high school teacher did not want to deal with the issue of what is happening when (b² – 4AC) – Expression under the square root in the square formula – negative. They may have cleaned this under the carpet as something to deal with it in the college.

However, if you are ready to believe that there are square roots of negative numbers, you will get solutions for a new set of spring equations. In fact, the amazing and completely useful mathematics world appears in the appearance: a world Complex analysis.

Complex numbers simplify other areas of mathematics

What do you get to your faith jump in complex numbers?

For anyone, trigonometry becomes much easier. Instead of saving many complex triangles formulas, you need only one equation for all of them: Alar 1740 formula. With decent algebra skills, you can process the Awler formula to see that most Standard triangular formulas Used to measure the length of the triangle or an angle that becomes early.

Calculator calculation is also easier. As mathematics Roger Cotsand Rene Descartes – Those who formulated the term “fictional number” – and others noticed, the complex numbers make the impossible integration apparently easy to solve and measure the area under complex curves.

Complex numbers also play a role in understanding all potential engineering characters that you can build with the ruler and compass. Mathematics also noted Jean Robert Argand and Karl Friedrich GaousYou can use complex numbers to treat engineering characters such as Pentagons and Octagons.

Complex analysis in the real world

Complex analysis has many applications on the real world.

Mathematics Rafael Pompeli The idea of ​​performing algebraic operations such as addition, subtraction, beating and division by complex numbers makes it possible to use them to calculate the differentiation and integration.

Hence, much of what scientists use physics to study signals – or data transmission – more management and understanding. For example, the complex analysis is used Tampering with wavesOr small fluctuations in data. This is necessary to remove noise in a distorted signal from the satellite, as well as pressure images to store the most efficient data.

The complex analysis allows engineers to convert a complex problem into an easier problem. Thus, it is also an important tool in many applied physics topics, such as studying electrical properties and fluids for complex structures.

Once they become more comfortable with complex numbers, famous mathematicians love Carl Wiresrasand Augustine Luis Kushi and Bernhard Riman Others were able to develop a complex analysis, and to build a useful tool that not only simplifies mathematics and progress in science, but also made it more understanding.

This article has been republished from ConversationAn independent, non -profit news organization brings you facts and trusted analysis to help you understand our complex world. Written by: William Rossand Richmond University

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William Ross does not work with, consulting, or receiving them from any company or institution that will benefit from this article, and has not been revealed by any related affiliations that exceed its academic appointment.