Let w = Reai be any nonzero complex number. Then w has n nth roots: n solutions to the equation z" = Reia or meine = Reia 2πTK n which have r = R¹/n and 0 = a + n R¹/n ei(a/n + 2π k/n), where k = 0, 1, 2, ..., n-1. The n nth roots of w are equispaced on the circle C of radius R¹/n centered at the origin. Draw the circle C, and then find the three 3rd roots of i. The circle C has radius 1 The nth roots of w are w¹/n = Z = The angle difference (in radians) between adjacent 3th roots is 2TT 3 Draw the circle C, and then find the four 4th roots of -16. The circle C has radius The angle difference (in radians) between adjacent 4th roots is Draw the circle C, and then find the two square roots (2nd roots!) of 1 + i. The circle C has radius . The angle difference (in radians) between adjacent square roots is X
Let w = Reai be any nonzero complex number. Then w has n nth roots: n solutions to the equation z" = Reia or meine = Reia 2πTK n which have r = R¹/n and 0 = a + n R¹/n ei(a/n + 2π k/n), where k = 0, 1, 2, ..., n-1. The n nth roots of w are equispaced on the circle C of radius R¹/n centered at the origin. Draw the circle C, and then find the three 3rd roots of i. The circle C has radius 1 The nth roots of w are w¹/n = Z = The angle difference (in radians) between adjacent 3th roots is 2TT 3 Draw the circle C, and then find the four 4th roots of -16. The circle C has radius The angle difference (in radians) between adjacent 4th roots is Draw the circle C, and then find the two square roots (2nd roots!) of 1 + i. The circle C has radius . The angle difference (in radians) between adjacent square roots is X
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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Transcribed Image Text:Let w = Reai be any nonzero complex number. Then w has n nth roots:
n solutions to the equation z = Reia or meine = Reia
which have r = R¹/n and 0 =
α
2TK
n
n
+
The nth roots of w are w¹/n
R¹/n ei(a/n + 2π k/n), where k = 0, 1, 2,
n-1.
The n nth roots of w are equispaced on the circle C of radius R¹/n centered at the origin.
Draw the circle C, and then find the three 3rd roots of i. The circle C has radius 1
2TT
The angle difference (in radians) between adjacent 3th roots is 3
= Z =
Draw the circle C, and then find the four 4th roots of -16. The circle C has radius
The angle difference (in radians) between adjacent 4th roots is
Draw the circle C, and then find the two square roots (2nd roots!) of 1 + i.
The circle C has radius
The angle difference (in radians)
between adjacent square roots is
X
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