301test2 - A-AE 301 Exam 1, Fall 2010. Please put your best...

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Unformatted text preview: A-AE 301 Exam 1, Fall 2010. Please put your best answer on the exam. Two pages of notes and no calculators. NAME: 1 Problem 1. Find the real and imaginary part of 4 + 6 i (1 + ) 2 = 1 i 2 i = 2 Problem 2. Compute the following i 6 (1- i ) 11 = 3 Problem 3. Plot in the complex plane (1+ ) e 4 for 0 / 4. Show the direction and the radius. 4 Problem 4. Find the set of all roots to the equation 3- 27 = 0. 5 Problem 5. Assume that t = k =- a k e- kti and t 2 = k =- b k e- kti (0 t 2) . Compute the following k =- a k b k = Problem 6. Suppose that g ( t ) admits a Fourier series expansion of the form g ( t ) = 2- 2 cos(2 t ) + 2 cos(5 t ) + 4 sin(80 t ) + 2 sin(109 t ) . Then find (be careful) 2 | g ( t ) | 2 dt = 6 Problem 7. Suppose that g ( t ) L 2 (0 , 4) admits a Fourier series expansion of the form g ( t ) = 3- 2 cos( t ) + 4 cos( t ) + 4 sin(2 t ) + 2 sin(4 t ) ....
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301test2 - A-AE 301 Exam 1, Fall 2010. Please put your best...

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