Mathematician believes that all expressions in maths have solution.
But there are equations that seems to be out of sort.
No solution looks fitting.
One example is shown below.
x - (x + 1)2 = 2
Here, by pure comparison without touching on mathematics, you can deduce that x is definitely smaller than ( x + 1).
Furthermore, what if the (x + 1) term is squared!
x is surely smaller than (x + 1)2 by this logically deduction.
Now the question, can x - (x + 1)2 be a POSITIVE number?
You will fully agree that it is impossible.
A smaller number minus a bigger number will give us a NEGATIVE outcome.
Then how do you get the answer to the above expression?
What is the "x" value that produces a positive "2"?
There is no way for any REAL number to satisfy this!
To solve this type of "impossible" equation, you need to venture into the "Complex Number" concept. Since real number cannot meet the criteria to resolve the maths question, you need to imagine a number to meet this task.
"Complex Number" consists of number formed by a REAL term and an IMAGINARY term.
It is this imaginary term that will give you an answer to the challenging question.
With the understanding of "imaginary number", you will be in a better position to appreciate the usefulness of solving any maths problem with complex number.
Maths is interesting, right?
When you cannot get an answer in the normal sense, you imagine a number!
What a way to get an answer.