The complex numbers.

Introduction

There are equations that have no solution in the set of real numbers. For example, the equation x ² +9 = 0 has no real solution because there is no real number squared give -9.

The Hindu mathematician Bhaskara (1114-1178) already referred in his book Lilavati to the absence of the square root of a negative number.

 
Gerolamo Cardano (1501-1576), Italian mathematician and physician, was the first to write the roots of negative numbers a solution of quadratic equation, although specifying that made no sense.

Euler (1707-1783) introduced a specific nomenclature to solve roots of negative numbers.

Carl Friedrich Gauss (1777-1855) completed the construction of a new set of numbers, the complex numbers.

 Complex numbers

Any complex number is an expression of the form a + bi where a is the real part and bi is the imaginary part. Both a and b are real and i=√(-1) .

Complex numbers appear to try to solve equations of the type x^2+1=0. Solving for x is obtained x=√(-1), which is write as  x = i.

Leonhard Euler who designed x=√(-1)  by the letter i. The symbol i expresses an accurately abstract idea.

Here i`ve attached two photos that represents the diferent forms of the complex numbers explained with a little exercise: