Question

What is the difference between real and imaginary roots?

Answer 1

Real roots can be expressed using only real numbers, while expressing imaginary roots requires using imaginary numbers.

Explanation:

Real roots can be expressed as real numbers. Sometimes this is simple, as with `sqrt4=2`, sometimes a bit more complex and we approximate, as with `sqrt3=1.7320508....` But always we are working in real numbers.

Imaginary roots are expressed in imaginary numbers, and the simplest imaginary number is `i=sqrt(-1)`. Most imaginary numbers can be expressed in the form '`a+bi` where `a` and `b` are real numbers, but the whole number is imaginary because of the presence of `i`.

We end up with imaginary roots when solving the equation involves taking the square root of a negative number.