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(Eisenstein arithmetic): Express your answers in the form x + yw. 2+5w-1-7w = (1 − w)5 = (2+3w). (5-w) = 0+1w +2w² +3w³ +4w¹ +...99w99 =

(Eisenstein arithmetic): Express your answers in the form x + yw. 2+5w-1-7w = (1 − w)5 = (2+3w). (5-w) = 0+1w +2w² +3w³ +4w¹ +...99w99 =

Advanced Engineering Mathematics
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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**Eisenstein Arithmetic: Express your answers in the form \( x + y\omega \).** 1. \( 2 + 5\omega - 1 - 7\omega = \underline{\hspace{2cm}} \) 2. \( (2 + 3\omega) \cdot (5 - \omega) = \underline{\hspace{4cm}} \) 3. \( (1 - \omega)^5 = \underline{\hspace{2cm}} \) 4. \( 0 + 1\omega + 2\omega^2 + 3\omega^3 + 4\omega^4 + \ldots + 99\omega^{99} = \underline{\hspace{4cm}} \)
Transcribed Image Text:**Eisenstein Arithmetic: Express your answers in the form \( x + y\omega \).** 1. \( 2 + 5\omega - 1 - 7\omega = \underline{\hspace{2cm}} \) 2. \( (2 + 3\omega) \cdot (5 - \omega) = \underline{\hspace{4cm}} \) 3. \( (1 - \omega)^5 = \underline{\hspace{2cm}} \) 4. \( 0 + 1\omega + 2\omega^2 + 3\omega^3 + 4\omega^4 + \ldots + 99\omega^{99} = \underline{\hspace{4cm}} \)
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