In basic algebra, the variables x and y generally stand for values of real numbers. It is intended to help the student, but will replace neither personal lecture notes nor a good textbook. I shall give the course in French, but if some student so wishes, I shall write on the blackboard in English. In the same eventuality, these lecture notes are in English. A complex random variable on the probability space (,,) is a function: → such that both its real part () and its imaginary part () are real random variables on (,,).. In the second phenomenon, i.e., crime and violence in the streets, the independent variable may be the number of law enforcers, and … TDP. Increased temperature will cause the expansion of water in the sea. Unlike calculus using real variables, the mere existence of a complex derivative has strong implications for the properties of the function. Several Complex Variables P. M. Gauthier March 14, 2006 Abstract This is a mere sketch of the course being given in the fall of 2004. Complex analysis is a basic tool with a great many practical applications to the solution of physical problems. For example, in the first phenomenon of climate change, temperature (independent variable) may influence sea level (dependent variable). Functions of a complex variable. Consider a random variable that may take only the three complex values +, −, with probabilities as specified in the table. The algebra of complex numbers (complex analysis) uses the complex variable z to represent a number of the form a + bi. This is a simple example of a complex random variable. This short tutorial is a companion material to the course on Functions of a Complex Variables . For examples of applications see Olver (1997b, pp. Complex variable, In mathematics, a variable that can take on the value of a complex number. Definition. 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