(a) The complex numbers w and z are given by w = -1 – j and z = 2+2j. (i) Determine arg(wz). (ii) Determine the Cartesian form of w14. Does this complex number have the same argument as wz?
(a) The complex numbers w and z are given by w = -1 – j and z = 2+2j. (i) Determine arg(wz). (ii) Determine the Cartesian form of w14. Does this complex number have the same argument as wz?
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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![(a) The complex numbers w and z are given by w = -1– j and z = 2+2j.
(i) Determine arg(wz).
(ii) Determine the Cartesian form of w14. Does this complex
number have the same argument as wz?
(b) De Moivre's theorem states that
[cos(0) + j sin(0)]" = cos(n0) + j sin(n®).
Using this theorem, or otherwise, evaluate
/3
I =
3 cos (0) sin(@) – sin*(Ø) d0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74c6003a-14d6-4ef6-9bf4-cc19142fa1f9%2F4fc24c53-1bbe-4c0f-9969-fd3f425234ad%2Fudfa6b_processed.png&w=3840&q=75)
Transcribed Image Text:(a) The complex numbers w and z are given by w = -1– j and z = 2+2j.
(i) Determine arg(wz).
(ii) Determine the Cartesian form of w14. Does this complex
number have the same argument as wz?
(b) De Moivre's theorem states that
[cos(0) + j sin(0)]" = cos(n0) + j sin(n®).
Using this theorem, or otherwise, evaluate
/3
I =
3 cos (0) sin(@) – sin*(Ø) d0.
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