Why Did Rafael Bombelli Believe In The Existence Of Imaginary Numbers

The formation and acceptance of i took several centuries and a series of individuals. For example, at first, for a very long time no one had tried to manipulate imaginary numbers. In fact, in 50 A.D., Heron of Alexandria deemed it impossible to solve for the square root of negative numbers. For instance, he was studying the volume of an impossible section of a pyramid and had to take √81-114. Heron of Alexandria thought it was impossible and gave up. However, it wasn’t because of the lack of trying hat he had given up. In fact, when negative numbers were “invented”, mathematicians had tried to find a number that when squared, would equal to a negative one. On the contrary, the mathematicians had failed to find an answer and gave up. But then,

In fact, Bombelli help introduce complex numbers. Even though, he really didn’t understand what to do with complex numbers, himself. Therefore, many people didn’t believe Bombelli. Although, he did understand that i times i should equal -1, and that –i times i should equal one. Thus, he provided the rules of multiplication to the complex numbers. Yet, many people didn’t believe this fact either. Lastly, he had a “wild idea”, that you could use imaginary numbers to get the real answers, which is now known as conjugation. Yet, Bombelli, himself, did not have much of an impact at the time, (since many people didn’t believe Bombelli nor his ideas), but he had help lead the way for imaginary

For example, one way these individuals wanted to make complex numbers was to plot them on a graph. For example, the x-axis would be real numbers and the y-axis would be imaginary numbers. If a number was a purely imaginary number it would be on the y-axis and if the number was a purely real number it would be on the x-axis. John Wallis was the first to consider this graph and give a geometrical representation of complex numbers. He believed a complex number is just a point on the number line, however he was ignored. Meanwhile, an individual named Caspar Wessel gives a modern geometric representation of the complex numbers by correctly representing complex numbers on a plane and observing that the complex numbers abandon the two directional lines. Wessel treats the complex numbers as vectors (without using the term). However, his ideas were also ignored. While, another individual named, L. Euler introduced i as the symbol for square root of negative one. In addition, Jean Robert Argand wrote how to plot these complex numbers in a plane. This is now known as Argand diagram. Then in 1831, Carl Friedrich Gauss made Argand’s idea popular and then took Descartes’ a+bi notation and called it a complex number. Lastly, William Rowan Hamilton expressed complex numbers as real numbers by expressing 4+3i as (4,3)) and thus making it