Augustin-Louis Cauchy (1789–1857)
If you love mathematics and have never studied complex function theory, then you are missing something wonderful. It is one of the most beautiful branches of maths, with many amazing results. Don’t be put off by the name: complex does not mean complicated. With elementary calculus and a basic knowledge of imaginary numbers, a whole world of wonder is within your grasp.
In the early nineteenth century, Augustin-Louis Cauchy (1789–1857) constructed the foundations of what became a major new branch of mathematics, the theory of functions of a complex variable.
of a real variable, we often have to find the values of 
for which the function is zero. A simple iterative method was devised by Isaac Newton and refined by Joseph Raphson. It is known either as Newton’s method or as the Newton-Raphson method. It usually produces highly accurate approximations to the roots of the equation 
.
, which obviously does not converge, but alternates between 
and 
.
