Imaginary numbers have a square that is a negative real number and are represented by the letter i. They were once thought to be fictitious but are now accepted and used in fields such as quantum mechanics and electrical engineering. They can be represented on a graph with the imaginary number axis perpendicular to the standard number line.
An imaginary number is a mathematical term for a number whose square is a negative real number. Imaginary numbers are represented with the letter i, which represents the square root of -1. This definition can be represented by the equation: i2 = -1. Any imaginary number can be represented using i. For example, the square root of -4 is 2i.
When imaginary numbers were first defined by Rafael Bombelli in 1572, mathematicians believed they didn’t actually exist, hence their name. Decartes coined the term imaginary in reference to these numbers in his 1637 book, La Geometrie. However, imaginary numbers are as real as any other number and have gradually been accepted by the mathematical community and the world at large. The work of mathematicians Leonhard Euler and Carl Friedrich Gauss in the 18th and 19th centuries was instrumental in this change.
While imaginary numbers are meaningless in the “real world” of most individuals, they are indispensable in fields such as quantum mechanics, electrical engineering, computer programming, signal processing, and cartography. For perspective, consider that even negative numbers were once thought to be fictitious, and that concepts like fractions and square roots might be considered meaningless to a person who has no need for them in day-to-day life, although they are real enough for others. .
To better understand imaginary numbers, geometry can be helpful. Imagine a standard number line: zero is in the center, positive numbers are to the right of zero, and negative numbers are to the left. At the zero point, it displays another line perpendicular to the first one, extending up and down instead of right and left. This is the imaginary number axis, also known as the y-axis in geometry, while the “standard number line” is the x-axis. Positive imaginary numbers extend upwards from the zero point and negative imaginary numbers extend downwards. Zero is the only number considered to be both real and imaginary.
Protect your devices with Threat Protection by NordVPN
