War and Peace

In the beginning there were natural numbers. People counted their sheep or cows starting with one. They could do simple additions and subtractions. And life was happy.

Then one day equations were invented - and the numbers are having a tough time to keep up ever since.

First came the simplest of all equations: x + 1 = 2
The numbers had an answer: x = 1

Wow!

Then came a complex equation: x + 2 = 1
The numbers were stumped!!! No number when added to 2 gives 1!
The numbers had to reinvent themselves.

Thus they gave birth to a new and tougher generation, integers.
Now x + 2 = 1 had a solution: x = -1

So far, so good.

Then came up a new equation: 2x = 3
Whoa!!! Now the numbers were again in trouble. They thought and thought and finally came up with rational numbers.
Now 2x = 3 had a solution: x = 3/2

So far, so good.

But, the equations were not going to give up.
They said: How about x*x = -1?
Too bad!
You multiply any number by itself, you are never going to get a negative number!
The numbers had to push themselves this time. They thought and thought and finally came up with i, the complex square root of -1!

(Of course, there were other equations that threatened the number system and the number system always won by creating more numbers, e.g. irrational numbers, transcendenatal numbers etc.)

Now the question is: Can the equations wage another war? Can you come up with an equation using the basic operations and existing numbers that does not have a solution in complex numbers? Can we say that the numbers have had the final victory?