Complex numbers are an extension to real numbers and extensively used in many aspects of mathematics relating to fields like engineering, electromagnetism, quantum physics, applied mathematics, and chaos theory.
A complex number is made up of two parts, a real part and an imaginary part. A general complex number would be a + ib where a is the real part and ib is the complex part with the coefficient b and i representing the square root of -1.
As you know any number when multiplied by itself gives a positive result. Then what would be the square root of a negative number? To accommodate this, the symbol i was introduced.
i = square root of -1 or i^2 = -1.
A complex number is drawn graphically on a system where the x-axis represents the real part and the y-axis represents the complex part.
Every equation has a root. If it does not intersect the x-axis where the x-y axes are real coordinates, it does not have a real root, instead it has complex roots.
There is no equation which does not have roots, they are either real or complex in nature.