The Complex Numbers
Imaginary and Complex Numbers
Negative numbers do not have square roots in the real-number system. However,
mathematicians have described a larger number system that contains
the real-number system, such that negative numbers have square roots. That
system is called the complex-number system.We begin by defining a number
that is a square root of -1. We call this new number i.
The Complex Number i
We define the number i to be 
. That is, i = and i2 = -1.
To express roots of negative numbers in terms of i we can use the fact that in the complex number, 
= 
= 
when p is a positive real number.
Imaginary Number
An imaginary* number is a number that can be named
bi,
where b is some real number and b ≠ o.
To from the system of complex numbers, we take the imaginary numbers and the real numbers and possible sums of real and imaginary numbers. These are complex numbers:
7 – 4i, i
.