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.
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