Problems on Complex Numbers From Old Exams

Thomas' Calculus: Early Transcendentals

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This homework help was uploaded on 02/12/2008 for the course MATH 104 taught by Professor Nelson during the Fall '07 term at Princeton.

Ask a homework question - tutors are online