Recall that i = √-1 € C, and let 0 € R. Prove that for all integers n ≥ 0, we have (cos+ i sin 0) = cos(n) + i sin(ne). You cannot use the fact that eie = cos 0+isin, or similarly anything involving e or polar coordinates. You will find the compound angle formulas helpful: for all a, ß ER, we have cos a cos 3- sin a sin 3 = cos(a + B), sin a cos 3 + cos a sin 3 = sin(a+ß).
Recall that i = √-1 € C, and let 0 € R. Prove that for all integers n ≥ 0, we have (cos+ i sin 0) = cos(n) + i sin(ne). You cannot use the fact that eie = cos 0+isin, or similarly anything involving e or polar coordinates. You will find the compound angle formulas helpful: for all a, ß ER, we have cos a cos 3- sin a sin 3 = cos(a + B), sin a cos 3 + cos a sin 3 = sin(a+ß).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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