Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
The polar form of –256 – 256V3i is 512 (cos (-) +i sin (-)) (for steps, see polar form calculator). According to the De Moivre's Formula, all n-th roots of a complex number 0+2rk r (cos (0) + i sin (0)) are given by ri (cos (+2nk ) + i sin (º+2ak )), k = 1 OS 0..n – 1. 27 We have that r = 512, 0 = -+2-7-0 • k = 0:STA(cos (=2) + i sin (=2*0) 2 (cos (-+ i sin (- • k = 1: 512 (cos (=1). 2 (cos + i sin ()) = 2 cos • k = 2: 512 (cos (=3-2) + 2 (cos k = 3: 512 (cos (-2) 2 (cos 4: 512 (cos COs 9. 2 cos 22 sin 27) +2-T-1 27. +i sin (-*1)) O + 2i sin +2-T-2 9. 4T 27 - +2-7-2 +i sin 9 10T 107 + i sin ()) 107 10T 2 cos () + 2i sin (0 i sin 27 27 +2-7-3 +2-7-3 COS 9. 9. 167 16T 11T + i sin -2 cos 27 + 2i sin 27 27 +i sin (-**)): +2-T-4 • k %3D 9. 签) k = 5: 512 (cos (=3) i sin ()) = 登+2-T-6 2 (cos 227 22T + i sin -2 cos 27 + 2i sin 27 +i sin (=* ;***)) : +2-7-5 +2-7-5 2 (cos 28T -2 cos () - 2i sin () 27 +i sin ( )) • k = 6: S12 (cos (=**) +i sin ()) 2 +2-7-7 +2-7-6 9. 2 (cos (347 •k = 7: 512 (cos -2 cos (E) – 2i sin (E + i sin (=*1)): -2 cos () - 2i sin ( -* +2-7-8 27 +2-7-7 9. 40T 137 2 (cos • k = 8: 512 (cos (=*) + 2 (cos +i sin ()) 40T 137 27 +2.T-8 9. Hi sin (27 – 2i sin () 46T 46t = 2 cos 27 27

The polar form of –256 – 256V3i is 512 (cos (-) +i sin (-)) (for steps, see polar form calculator). According to the De Moivre's Formula, all n-th roots of a complex number 0+2rk r (cos (0) + i sin (0)) are given by ri (cos (+2nk ) + i sin (º+2ak )), k = 1 OS 0..n – 1. 27 We have that r = 512, 0 = -+2-7-0 • k = 0:STA(cos (=2) + i sin (=2*0) 2 (cos (-+ i sin (- • k = 1: 512 (cos (=1). 2 (cos + i sin ()) = 2 cos • k = 2: 512 (cos (=3-2) + 2 (cos k = 3: 512 (cos (-2) 2 (cos 4: 512 (cos COs 9. 2 cos 22 sin 27) +2-T-1 27. +i sin (-*1)) O + 2i sin +2-T-2 9. 4T 27 - +2-7-2 +i sin 9 10T 107 + i sin ()) 107 10T 2 cos () + 2i sin (0 i sin 27 27 +2-7-3 +2-7-3 COS 9. 9. 167 16T 11T + i sin -2 cos 27 + 2i sin 27 27 +i sin (-**)): +2-T-4 • k %3D 9. 签) k = 5: 512 (cos (=3) i sin ()) = 登+2-T-6 2 (cos 227 22T + i sin -2 cos 27 + 2i sin 27 +i sin (=* ;***)) : +2-7-5 +2-7-5 2 (cos 28T -2 cos () - 2i sin () 27 +i sin ( )) • k = 6: S12 (cos (=**) +i sin ()) 2 +2-7-7 +2-7-6 9. 2 (cos (347 •k = 7: 512 (cos -2 cos (E) – 2i sin (E + i sin (=*1)): -2 cos () - 2i sin ( -* +2-7-8 27 +2-7-7 9. 40T 137 2 (cos • k = 8: 512 (cos (=*) + 2 (cos +i sin ()) 40T 137 27 +2.T-8 9. Hi sin (27 – 2i sin () 46T 46t = 2 cos 27 27

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
See similar textbooks
icon
Related questions
Question
How did the value on the red circles became like that from the original equation on the blue circle? Please explain.
The polar form of –256 – 256/3i is 512 (cos (-) +i sin (-)) (for steps, see polar form calculator). According to the De Moivre's Formula, all n-th roots of a complex number 1 r (cos (0) + i sin ()) are given by ri (cos (2nk) + i sin (+2nk ). k = 0+2™k 0..n – 1. 27 We have that r = 512, 0 = 3 arTa -+2-7-0 • k = 0:STA(cos (=2) + i sin (=:2*0) 2 (cos (-+ i sin (- COs 9. 2 cos 27 sin 27) +2-T-1 27. • k = 1: 512 (cos (=1). 2 (cos + i sin ()) = 2 cos - +2-7-2 • k = 2. 512 (cos (=3=2) + +i sin ()) + i sin (1)) O + 2i sin '-좋+2·T-2 * +2-T-1 4T 27 +i sin 9 2 (cos 107 107 107 10T 2 cos () + 2i sin 27 27 27 k = 3: 512 (cos (-23) + i sin ()) +2.7-3 +2-7-3 COS + i sin 9. 2 (cos 167 16t 11T -2 cos 27) + 2i sin 27 = 27 k = 4: 512 (cos (=+24) +i sin (-* **4)): +2-7-4 • k 9. 登)) k = 5: 512 (cos (=) 2 (cos 22T 22т 57 +i sin -2 cos 27 + 2i sin 27 +i sin (-*)) : i sin ()) = -2 cos () – 2i sin (A) + i sin (-***)) +2-T-5 +2-T-5 2 (cos '28ㅠ 27 27 • k = 6: 512 (cos (=*) +i sin ()) - 2 +2-T-7 空+2-7-6 +2-7-6 34т 2 (cos -2 cos (E) – 2i sin (E - 2 +2.T-7 27 • k = 7: 512 ( cos +i sin 9. 40™ 9. 2 (cos • k = 8: 512 (cos (=3*) 2 (cos 13™ +i sin ()) -2 cos () – 2i sin () - +2-7-8 40л 137 27 + i sin (-*) = +2.T•8 9. Hi sin (*27 – 2i sin () 46T 46т = 2 cos 27 27 ||
Transcribed Image Text:The polar form of –256 – 256/3i is 512 (cos (-) +i sin (-)) (for steps, see polar form calculator). According to the De Moivre's Formula, all n-th roots of a complex number 1 r (cos (0) + i sin ()) are given by ri (cos (2nk) + i sin (+2nk ). k = 0+2™k 0..n – 1. 27 We have that r = 512, 0 = 3 arTa -+2-7-0 • k = 0:STA(cos (=2) + i sin (=:2*0) 2 (cos (-+ i sin (- COs 9. 2 cos 27 sin 27) +2-T-1 27. • k = 1: 512 (cos (=1). 2 (cos + i sin ()) = 2 cos - +2-7-2 • k = 2. 512 (cos (=3=2) + +i sin ()) + i sin (1)) O + 2i sin '-좋+2·T-2 * +2-T-1 4T 27 +i sin 9 2 (cos 107 107 107 10T 2 cos () + 2i sin 27 27 27 k = 3: 512 (cos (-23) + i sin ()) +2.7-3 +2-7-3 COS + i sin 9. 2 (cos 167 16t 11T -2 cos 27) + 2i sin 27 = 27 k = 4: 512 (cos (=+24) +i sin (-* **4)): +2-7-4 • k 9. 登)) k = 5: 512 (cos (=) 2 (cos 22T 22т 57 +i sin -2 cos 27 + 2i sin 27 +i sin (-*)) : i sin ()) = -2 cos () – 2i sin (A) + i sin (-***)) +2-T-5 +2-T-5 2 (cos '28ㅠ 27 27 • k = 6: 512 (cos (=*) +i sin ()) - 2 +2-T-7 空+2-7-6 +2-7-6 34т 2 (cos -2 cos (E) – 2i sin (E - 2 +2.T-7 27 • k = 7: 512 ( cos +i sin 9. 40™ 9. 2 (cos • k = 8: 512 (cos (=3*) 2 (cos 13™ +i sin ()) -2 cos () – 2i sin () - +2-7-8 40л 137 27 + i sin (-*) = +2.T•8 9. Hi sin (*27 – 2i sin () 46T 46т = 2 cos 27 27 ||
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS