## Example 1.1.7 (d): Simple Complex Numbers |

Which complex number |

The symbol *i* has the property that
*i ^{2} = -1*. Translating that property into the
language or our definition means that we are looking for a number

(x,y)*(x,y) = (x*x-y*y,xy + yx) = (-1, 0)

which results in the system of equations

(1) x*x-y*y = -1

(2) 2xy = 0

The second equation means that either *x = 0* or *y = 0*
or both. But together with the first equation we see that *y* can
not be zero so that:

x = 0andy = 1

Therefore the symbol *i* corresponds to the complex number
*(0,1)*.