Can someone explain complex zeros and the imaginary unit (i)?

Question

anonymous · Answer

Well, suppose you are solving a quadratic equation and 4ac > b^2.  What can you do to take the square root of a negative number?  You define i as the by saying that i times i equals -1.

anonymous · Answer

So like 1+3i would be 1+3sqrt(-1)?

anonymous · Answer

Yes

anonymous · Answer

So then you can just factor i out of negative square roots.

anonymous · Answer

sorry I'm kind of confused what you mean! If I factored it wouldn't it be i?

anonymous · Answer

Oh do I have to multiply it by 1-3i?

anonymous · Answer

The simplest application is like this.  We have
ax^2 + bx + c and plug into the quadratic formula and find that 
b^2 - 4ac < 0, so how to do the square root?  i allows us to do this..

For example, if we have sqrt(-3), this equals i times sqrt(3).  That's our answer.

A more "complex" example is the complex number 1 - 3i.  There are rules to do algebra with complex numbers (and more, logarithms, exponentials) but this is more than you need, I think.