**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 i^{2} = -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.