i is called the imaginary number and it's defined as the square root of -1. Thus we can say the following is true:

     i * i = -1

     There's an easy way to understand multiplication by i. Since i is the square root of -1 then i * i (or i²) is equal to -1. -i is the same as -1 * i so problems like -i * -i can be thought of as -1 * i * -1 *i or -1 * -1 * i * i which becomes 1 * i * i and then i * i, which we already have an answer for.

     i*i = -1
     -1*i = -i
     -i*i = -1*i*i = -1*-1 = 1
     -i*-i = -1*-1*i*i = 1*i*i = i*i = -1

     x*i, where x is any real constant, is usually written as xi.

     1*i = i
     2*i = 2i
     3*i = 3i
     4*i = 4i
     5*i = 5i
     6*i = 6i
     7*i = 7i
     8*i = 8i
     9*i = 9i
     10*i = 10i
     11*i = 11i

     Numbers that are part real and part imaginary, like 5 + 6i, are normally written in two ways. 5 + 6i can be written as either 5 + 6i or (5,6). Numbers that are both real and imaginary are called complex numbers. Complex numbers are often plotted on a 2 dimansional graph where the x-position is the real part and the y-position is the imaginary part.

That's odd?

Calculating ii Calculating ln(i)

What's It Good For?

i	Calculating the Trig Functions

More Resources

i Explained By Dr. Math