The equation is known as quadratic equation in one variable where
i.e., we get the roots in real numbers.
Let’s take the equation , where
, this is not a real number, i.e., for a quadratic equation
where
<
, we can’t get a real roots for this. So we can take
, is the imaginary number to find out the root of the equation
.
Hence , in the quadratic equation
we get two imaginary roots.
Complex Number:
The number which is of the form , where
and
are real numbers is defined to be a complex number.
We also take , where
is the real part, denoted by
and
is the imaginary part denoted by
.
The set consists of all the complex numbers is called a complex number set or set of complex numbers and denoted as .
For example,
,
Here
Two complex numbers and
are equal iff
and
Example:
If , where
and
are real numbers, then find the value of
and
.
Solution:
(Given)