Chapter 1 - Numbers MM - Page 13 of 14 |Numbers - Imaginary
Numbers - Contents| Outside the set of real numbers is the set
of imaginary numbers. They use a mathematical contrivance that
allows for taking the square root of a negative number. The
letter i (j in electrical engineering) usually represents a
special imaginary number. This number is equal to the square
root of negative one. It then makes it possible to solve
equations such as x squared equals negative one. Before
imaginary numbers there is not a solution. With them, x can
equal positive i or negative i as a solution. The set of
imaginary numbers consists of i times every number in the set of
real numbers. These two mirrored sets, combined in the equation
form z = a + bi, create the complex numbers. Here a is a
constant real number and b is a constant real number times i the
special imaginary number. A coordinate system with the
horizontal axis the set of real numbers and the vertical axis
the set of imaginary numbers are used to map complex number