Complex numbers and function. - a historic journey. (From Wikipedia, the free encyclopedia). Contents. Complex numbers Diophantus Italian rennaissance mathematicians Rene Descartes Abraham de Moivre Leonhard Euler Caspar Wessel Jean-Robert Argand Carl Friedrich Gauss.
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- a historic journey
(From Wikipedia, the free encyclopedia)
Collection of taxes
Right angled triangle
Perimeter = 12 units
Area = 7 square units
Made translations of Diophantus’ books
Calculated with negative numbers
Rules for addition, subtraction and multiplication of complex numbers
Lets try to put in the number 4 for x
64 – 60 – 4 = 0
We see that 4 has to be the root (the positive root)
Cardano’s formula gives:
Bombelli found that:
On the analytic representation of direction
The modulus is:
The argument is:
Then (by Wessels discovery):
Gauss had a profound influence in many fields of mathematics and science
Ranked beside Euler, Newton and Archimedes as one of history's greatest mathematicians.
Every complex polynomial of degree n has exactly n roots (zeros), counted with multiplicity.
(where the coefficients a0, ..., an−1 can be real or complex numbers), then there exist complex numbers z1, ..., zn such that
The theorem is usually formulated for closed paths as follows: let U be an open subset of C which is simply connected, let f : U -> C be a holomorphic function, and let γ be a path in U whose start point is equal to its endpoint. Then
Let f(x + iy) = u + iv
Then f is holomorphic if and only if u and v are differentiable and their partial derivatives satisfy the Cauchy-Riemann equations