Show that for z, w € C: |z − w|² = |2|² + |w|² - 2 Re(wz). Sketch the set of complex numbers z EC satisfying the equation |2|² - 2 Re((1 - i)2) = 0. [Hint: use (a) with w=1+i.]
Show that for z, w € C: |z − w|² = |2|² + |w|² - 2 Re(wz). Sketch the set of complex numbers z EC satisfying the equation |2|² - 2 Re((1 - i)2) = 0. [Hint: use (a) with w=1+i.]
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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![2. (a) Show that for z, w € C:
|z − w|² = |z|² + |w|² - 2 Re(wz).
(b) Sketch the set of complex numbers z EC satisfying the equation
|z|² - 2 Re((1 - i) z) = 0.
[Hint: use (a) with w = 1+ i.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F490cbcd2-ad81-426b-824f-903aced284ba%2F1a738585-edb1-4745-ad33-a73abf3c5331%2Fel44lxe_processed.png&w=3840&q=75)
Transcribed Image Text:2. (a) Show that for z, w € C:
|z − w|² = |z|² + |w|² - 2 Re(wz).
(b) Sketch the set of complex numbers z EC satisfying the equation
|z|² - 2 Re((1 - i) z) = 0.
[Hint: use (a) with w = 1+ i.]
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