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4. Let = || (cos 0+isin) € C be any complex number. The following formula: 0+2km 9+2km), k= 0, 1, 2,..., n-1 VET (COS cos 11 +isin- gives the n nth roots of : in C. Use it to solve each of the following equations. (a) =5+32=0 (c) w³=i (b) w = (-1+i) (d) 5+²=0

4. Let = || (cos 0+isin) € C be any complex number. The following formula: 0+2km 9+2km), k= 0, 1, 2,..., n-1 VET (COS cos 11 +isin- gives the n nth roots of : in C. Use it to solve each of the following equations. (a) =5+32=0 (c) w³=i (b) w = (-1+i) (d) 5+²=0

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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4. Let z = || (cos+isin) € C be any complex number. The following formula: VIEI (cos+ 2km n gives the n nth roots of z in C. Use it to solve each of the following equations. (a) 25+32-0 (c) w³=i (b) w = (-1+i) (d) 5+²=0 +isin +2km), n k = 0, 1, 2,..., n-1
Transcribed Image Text:4. Let z = || (cos+isin) € C be any complex number. The following formula: VIEI (cos+ 2km n gives the n nth roots of z in C. Use it to solve each of the following equations. (a) 25+32-0 (c) w³=i (b) w = (-1+i) (d) 5+²=0 +isin +2km), n k = 0, 1, 2,..., n-1
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