relating

[jlcowgill]

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

[uncool]

Imaginary numbers are the square roots of negative real numbers.

 

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

-Uncool-

[Dave]

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.

[BigMoosie]

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