The set of complex numbers is two-dimensional and a coordinate plane is needed to illustrate them graphically. This is different from real numbers, which are one-dimensional and can be represented by a simple number line. The plane of rectangular complex numbers is constructed by arranging the real numbers along the horizontal axis and the imaginary numbers along the vertical axis. Each point in this plane can be assigned a unique complex number, and each complex number can be assigned to a unique point in the plane. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an Original Essay A complex number really tracks two things at once. One of these things is the real part while the other is the imaginary part. For example, z = 3 + 2i is a complex number. The real part of z is 3 and the imaginary part of z is 2. The everyday meaning of "imaginary" is something that does not exist. The meaning in mathematics is quite different. Identifying the imaginary part of a complex number is easy because it has a label. The imaginary part is the number that multiplies the label i'. The imaginary part of 3 + 2i is 2. Be careful because the imaginary part is not 2i. The imagery does not include the label. At first, solving problems like "√-39" and "x2+1=0" was impossible. However, mathematicians soon got the idea that such a number could be created to solve these equations. The number is √-1, known as i. It is a good thing that scientists, mathematicians who did not want the creation of a new number, and other non-believers have finally admitted i's (and complex numbers) into the number system. The “i” is very useful in the world today. "i" is an extraordinary number. It is the only imaginary number until you square it and then it becomes real. However it was not created instantly, it took several centuries to convince some mathematicians to accept this new number. Eventually, though, a section of numbers called “imaginary” numbers was created (which also includes complex numbers, which are numbers that have both a real and an imaginary part), and people were now using i in everyday mathematics . emerged when Hero of Alexandria, a Greek mathematician, was trying to evaluate the square root of a negative number. He later discovered that the square root of a negative number cannot be calculated using only real numbers. To find a solution it was necessary to invent another new number system. In the mid-16th century, an Italian mathematician named Girolamo Cardano began doing just that. He is recognized as the discoverer of imaginary numbers which play an essential role in understanding the complex number system. Carl Friedrich Gauss, a nineteenth-century German mathematician, is considered the inventor and name of the complex number system. Complex numbers are generally expressed in the form a + bi, where a and b are real numbers and ei is the imaginary number. The “a” part is considered the real part of the complex number and the “bi” part is the imaginary part of the complex number. Upon closer inspection, we can see that the set of complex numbers includes all the pure real numbers, along with all the pure imaginary numbers, along with many other numbers that are sums of these. In other words, whenever a complex number has b = 0, it is actually also a pure real number because it is equal to a + 0i, which is simply a real number. Whenever a complex number has a = 0, it is actually a pure imaginary number because it is equal to 0 + bi, which is simply bi, an imaginary number. Electrical engineers often use complex numbers in their calculations every day. For example, when electricity flows through an electrical circuit component such as a.