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L'Algebra by Rafael Bombelli: frontispiece of the Bologna edition of 1579. Rafael Bombelli (baptised on 20 January 1526; died 1572) [a] [1] [2] was an Italian mathematician.Born in Bologna, he is the author of a treatise on algebra and is a central figure in the understanding of imaginary numbers.
An imaginary number is the product of a real number and the imaginary unit i, [note 1] which is defined by its property i 2 = −1. [1] [2] The square of an imaginary number bi is −b 2. For example, 5i is an imaginary number, and its square is −25. The number zero is considered to be both real and imaginary. [3]
A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1.
Leonhard Euler (/ ˈ ɔɪ l ər / OY-lər; [b] German: [ˈleːɔnhaʁt ˈʔɔʏlɐ] ⓘ, Swiss Standard German: [ˈleɔnhard ˈɔʏlər]; 15 April 1707 – 18 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of ...
All rational numbers are real, but the converse is not true. Irrational numbers (): Real numbers that are not rational. Imaginary numbers: Numbers that equal the product of a real number and the imaginary unit , where =. The number 0 is both real and imaginary.
The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation x 2 + 1 = 0. Although there is no real number with this property, i can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of i in a complex number is 2 + 3i.
Image credits: Wichella #8. Can only remember a moment in personal history. I was the last generation in my country to do mandatory military service. And apparently my generation is particularly lazy.
In 1871 Richard Dedekind called a set of real or complex numbers which is closed under the four arithmetic operations a field. In 1873 Maxwell presented A Treatise on Electricity and Magnetism . In 1878, William Kingdon Clifford published his Elements of Dynamic . [ 76 ]