Summary:
Complex numbers, and more specifically the number i, made an early appearance
in the history of Mathematics in the 16th century, when Italian mathematicians
were trying finding ways to solve square equations. In 1572 Rafaello Bombelli,
the last great mathematician of Bologna, presented his book Algebra and as he
was studying the square roots of various numbers, he faced an unanswered
question: ‘Which is the square root of the negative number -1?’ The solution
was to create a completely new number which would be by definition the answer
to this question. This peculiar number, which was characterized by Descartes as
imaginaire, appeared without being accompanied by a generally accepted symbol.
So, the imaginary number was born in the 16th century but acquired its
universal symbol i in the 18th century, after Euler’s proposition.
Apart from their significant applications in equations’ solutions, complex
numbers can be also subjects of study for several mathematic units like number
systems, vectors, trigonometry can be well combined and lean to easy proofs and
logic generalisations of many theorems, for example the Simson’s, Napoleon’s
and Morley’s theorems. The present work is dealing with this issue.
Keywords:
Complex numbers, Geometry, Morley's Theorem, The nine points circle, Feuerbach's Theorem
