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Introduction : In elementary courses you learneda bout the existence, and some of the properties, of complex numbers. But in courses in calculus, it is most likely that you did not even see a complex number. In this text we study nothing but complex numbers and the calculus of functions of a complex variable. We begin with an in-depth examination of the arithmetic and algebra of complex numbers.     

Definition 1 : A complex number is any number of the form where a and b are real numbers and i is the imaginary unit.