6. (a) Show that for all complex numbers z and w |z - w? + |z + w? = 2|2[² + 2|w/*. %3D (b) Let u, v be complex numbers such that |u| = |v| =1 and |u – v| = 2. Use part (a) to express u in terms of v.
6. (a) Show that for all complex numbers z and w |z - w? + |z + w? = 2|2[² + 2|w/*. %3D (b) Let u, v be complex numbers such that |u| = |v| =1 and |u – v| = 2. Use part (a) to express u in terms of v.
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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![6.
(a) Show that for all complex numbers z and w
|z – w? + ]z + w? = 2|z|² + 2\w]*.
(b) Let u, v be complex numbers such that |u| = |v| =1 and |u – v| = 2.
Use part (a) to express u in terms of v.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc461a58-107a-4033-b04c-578dc11a9677%2Fb92f81ee-354d-42b3-a98b-2be773407a43%2Ftfo37m_processed.png&w=3840&q=75)
Transcribed Image Text:6.
(a) Show that for all complex numbers z and w
|z – w? + ]z + w? = 2|z|² + 2\w]*.
(b) Let u, v be complex numbers such that |u| = |v| =1 and |u – v| = 2.
Use part (a) to express u in terms of v.
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