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

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.

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.

List of most recently solved mathematics problems.

Jul 04, 2018

Limit (Calculus)

Evaluate $\displaystyle \large \lim_{x \,\to\, \tan^{-1}{3}} \normalsize {\dfrac{\tan^2{x}-2\tan{x}-3}{\tan^2{x}-4\tan{x}+3}}$

Jun 23, 2018

Limit (Calculus)

Evaluate $\displaystyle \large \lim_{x \to 0} \normalsize \dfrac{e^{x^2}-\cos{x}}{x^2}$

Jun 22, 2018

Integral Calculus

Evaluate $\displaystyle \int \dfrac{1+\cos{4x}}{\cot{x}-\tan{x}} dx$

Jun 21, 2018

Limit

Evaluate $\displaystyle \large \lim_{x \to \infty} \normalsize {\sqrt{x^2+x+1}-\sqrt{x^2+1}}$

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.