What does "i" represent? If the graph of an equation does not intersect the x-axis does it mean it has no roots?

Expert Answers
justaguide eNotes educator| Certified Educator

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.