Imaginary & Complex Numbers

Imaginary and Complex numbers are numbers that cannot be expressed as a real number. An imaginary number is a number that when squared equals a negative number. A complex number is a number that includes both a real and imaginary component.

Imaginary numbers were first used by Italian mathematician Gerolamo Cardano in the 16th century. He used them to solve cubic equations. Complex numbers were first used by the Swiss mathematician Leonhard Euler in the 18th century. He used them to solve equations that involving trigonometric functions.

Because imaginary and complex numbers cannot be expressed as a real number, they are often used in solving mathematical problems that cannot be solved using real numbers alone. For example, imaginary numbers can be used to find the square root of a negative number, which is not possible using real numbers alone. Similarly, complex numbers can be used to solve equations that have no real solution, such as the equation x^2 + 1 = 0.