What is the difference between complex numbers and real numbers?

The 'real numbers" are probably what you are familiar with: they include all the whole numbers (including negatives) like 1 and 2 and -43, plus all fractions, and even the "irrational" numbers such as square roots and pi.

The complex numbers include the real numbers plus a lot more. (It might help if you now think of numbers not as "actual" objects, but rather as things we construct).

The reason we construct complex numbers is because we want to solve various equations for X like

p(X) = 0,

where p(X) is a polynomial, and we can't do this all the time with the "real numbers" you learn about in high school.

For example, there is the equation

x^2 +1 = 0.

Solving this over the "real numbers" would mean finding a square root of -1. But as you probably know, you can't find the square root of a negative number! at least not among the "real" numbers you learnt about in high school. So we construct a new number which we call I, that satisfies this equation. In other words, we simply say I is the square root of minus one.

Then the complex numbers are all the numbers you can get by multiplying real numbers by I, and by adding the result to other real numbers,
i.e. everything of the form A+Bi, where A and B are real numbers.

The point is, that with the complex numbers you can solve any equation of the form

p(X) =0, where p is a polynomial with complex numbers as coefficients,

(although there may be no straightforward way of doing this).

I hope this helps a little.

Hi, PvPatel,
The answer before mine is good.
If you think of Real Numbers as said, like 2, 4, etc, even -2, -4, these types of numbers are answers to equations, that make the equation true.
Such as Square Root of 4 = + - 2. If you square +2, you get 4. If you square -2, you still get 4.

Complex numbers are those with no "real" answer.
Such as : Square Root of -4. There is no real number that you can square and get -4.
So, Complex Numbers use I. such as 2i. as explained in your first answer.
Best of luck.

Both of these answers are good, but too general, if your question is project related, please inform me, by using this email [email protected]