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Note for MATH 322 with Professor Glickenstein at UA

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This 1 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 22 views.

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Date Created: 02/06/15
Complex Numbers Check your knowledge D Are you comfortable with the following algebraic manipulations 0 Addition subtraction multiplication and division of complex numbers 0 Finding the real and imaginary parts and the modulus of combinations of complex numbers 0 Simplifying expressions that involve z and its complex conjugate 0 Going back and forth between polar and Cartesian representations of a complex number 0 Finding the argument roots logarithm exponential powers of a complex number 0 Given a complex number 2 can you evaluate the principal value at z of each of the multi valued functions we discussed in class D Do you know the definitions of the cosine sine hyperbolic cosine and hyperbolic sine of a complex number Do you know what De Moivre s formula and Euler s formula say Do you know them well enough to think of using them in a calculation D Do you know what the triangle inequality is D Do you know the definitions of the following concepts open neighborhood limit continuity and differentiability D Can you calculate limits or derivatives by following different paths in the complex plane D Can you use the definition of continuity to decide whether a function is continuous at a particular point D Can you find the derivative of a function by taking the limit of a difference quotient D Can you calculate derivatives of functions using the chain product or quotient rules D Do you know the definitions of the following terms differentiable analytic entire D Do you know what the CauchyRiemann equations are and how to apply them to decide whether a function is analytic D Do you know how to check whether a function is harmonic and if so do you know how find its harmonic conjugate Are you able to then write an expression for the resulting analytic function in terms of the complex variable 2 x 139 y

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