can somebody please tell me how the real numbers, imag. numbers, and complex numbers to each other. this was a question that was asked to me and i didn't know the answer

 

thanks joe

Imaginary numbers are the square roots of negative real numbers.

 

Complex numbers are the sum of real numbers and imaginary numbers.

-Uncool-

First you need to define the imaginary number i. Basically, i is just a number such that [imath]i^2 = -1[/imath]. Then a purely imaginary number is a number of the form [imath]ni[/imath] where n is just some real number. The complex numbers are numbers of the form [imath]m+ni[/imath] where this time you have some other number m in the reals.

 

Purely imaginary numbers aren't all that interesting. You can't do much with them (closure under multiplication, for one) but the complex numbers can exhibit some rather rich properties.

It annoys me that there exists a term imaginary number, all "purely imaginary" numbers should be called "simple complex" numbers.