Problems on Complex Numbers From Old Exams

Thomas' Calculus: Early Transcendentals

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Mat104 Problems on Complex Numbers From Old Exams (1) Find all solutions of z 5 = 6 i . (2) Find the real part of (cos 0 . 7 + i sin 0 . 7) 53 . (3) Find all complex numbers z , in Cartesian (rectangular) form such that ( z - 1) 4 = - 1. (4) Write ( 3 + i ) 50 in polar and in Cartesian form. (5) Find all fifth roots of - 32. (6) Write the following in Cartesian form a + ib where a and b are real and simplified as much as possible: (a) 1 1 + i + 1 1 - i (b) e 2+ iπ/ 3 (7) Write all solutions of z 3 = 8 i in polar and Cartesian form, simplified as much as possible. (8) Find all complex solutions of the equation z 5 = 1 + i . (9) Find the imaginary part of
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Unformatted text preview: 2 + i 3-i . (10) Find the angle between 0 and 2 π that is an argument of (1-i ) 1999 . (11) Find all z such that e iz = 3 i . (12) Write (1-i ) 100 as a + ib with a and b real numbers and simplify your answer. (13) Find the real part of e (5+12 i ) x where x is real, and simplify your answer. (14) Find all solutions to z 6 = 8 and plot them in the complex plane. (15) Evaluate ∞ X n =0 sin nθ n ! . (16) For what θ does ∞ X n =0 cos nθ 2 n converge? If it converges, what does it converge to? 1...
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