Complex Analysis
The study of functions of a complex variable is known as complex analysis and has enormous practical use in applied mathematics as well as in other branches of mathematics. Often, the most natural proofs for statements in real analysis or even number theory employ techniques from complex analysis (see prime number theorem for an example). Unlike real functions, which are commonly represented as two-dimensional graphs, complex functions have four-dimensional graphs and may usefully be illustrated by color coding a three-dimensional graph to suggest four dimensions, or by animating the complex function's dynamic transformation of the complex plane.
Read more about this topic: Complex Number
Famous quotes containing the words complex and/or analysis:
“Young children constantly invent new explanations to account for complex processes. And since their inventions change from week to week, furnishing the “correct” explanation is not quite so important as conveying a willingness to discuss the subject. Become an “askable parent.””
—Ruth Formanek (20th century)
“Ask anyone committed to Marxist analysis how many angels on the head of a pin, and you will be asked in return to never mind the angels, tell me who controls the production of pins.”
—Joan Didion (b. 1934)