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Imaginary unit

A solution to the quadratic equation $x^2+1 = 0$ is called the imaginary unit. It is also called as the unit imaginary number.

Introduction

A quadratic equation is a second degree polynomial equation and it can be solved mathematically to obtain roots of them, whereas it is not possible to find roots of a quadratic equation in a case.

$x^2+1 \,=\, 0$ is a quadratic equation and try to solve this equation.

$\implies x^2 \,=\, -1$

$\implies x \,=\, \pm\sqrt{-1}$

Therefore, $x \,=\, \sqrt{-1}$ and $x \,=\, -\sqrt{-1}$ are solutions of this quadratic equation.

Actually, there is no negative numbers but we created them for our convenience by displaying a negative sign before the natural numbers. Hence, it is not possible to find the square root of any negative number.

Representation

A Swiss mathematician Leonhard Euler understood it and imagined a unit for it. He proposed iota symbol to represent the square root of negative one and it is usually written as $i$ in mathematics.

$i \,=\, \sqrt{-1}$

Thus, the symbol $i$ is called as the imaginary unit or unit imaginary number in mathematics.