Imaginary number

[5] Although the Greek mathematician and engineer Heron of Alexandria is noted as the first to present a calculation involving the square root of a negative number,[6][7] it was Rafael Bombelli who first set down the rules for multiplication of complex numbers in 1572.

[8][9] The use of imaginary numbers was not widely accepted until the work of Leonhard Euler (1707–1783) and Carl Friedrich Gauss (1777–1855).

The geometric significance of complex numbers as points in a plane was first described by Caspar Wessel (1745–1818).

At 0 on the x-axis, a y-axis can be drawn with "positive" direction going up; "positive" imaginary numbers then increase in magnitude upwards, and "negative" imaginary numbers increase in magnitude downwards.

[12] In this representation, multiplication by i corresponds to a counterclockwise rotation of 90 degrees about the origin, which is a quarter of a circle.

[14] For example, if x and y are both positive real numbers, the following chain of equalities appears reasonable at first glance: But the result is clearly nonsense.