Essentials of Mathematical Methods in Science and Engineering, 2nd Edition

CHAPTER 9COMPLEX NUMBERS AND FUNCTIONS

As Gamow mentioned in his book, One Two Three … Infinity: Facts and Speculations of Science, the sixteenth‐century Italian mathematician Cardan is the first brave scientist to use the mysterious number called the imaginary with the property in writing. Cardan introduced this number to express the roots of cubic and quartic polynomials, albeit with the reservation that it is probably meaningless or fictitious. All imaginary numbers can be written as proportional to the imaginary unit . It is also possible to define hybrid numbers, , which are known as complex numbers.

Complex analysis is the branch of mathematics that deals with the functions of complex numbers. A lot of the theorems in the real domain can be proven considerably easily with complex analysis. Like control theory and signal analysis, many branches of science and engineering make widespread use of the techniques of complex analysis. As a mathematical tool, complex analysis offers tremendous help in the evaluation of series and improper integrals encountered in physical theories. ...