You can use one 8. 5 11 note sheet but no books or calculators are allowed. In order to receive credit for a problem you need to show enough work to justify your answer. Mathematics 300 final exam, april 27, 2006 (6 marks) problem 1: find all complex solutions to the equation cos(z) = 2i sin(z). Express each solution in the form z = x + yi, where x and y are real numbers. 3 (6 marks) problem 2: answer true or false to the following statements. Give valid reasons for all your answers. (a) log(z2) = 2 log(z) for every complex number z. If f (z) is not identically zero in any disc centered at z0 then g(z) = f (z) f (z) has a simple pole at z0. Mathematics 300 final exam, april 27, 2006 (6 marks) problem 3: find all singularities of the function f (z) = z.
