21. Given that z is a complex number satisfying |2z - 1|=|z2|, prove that |z| = 1 by: (a) letting z = x+iy, (b) squaring the equation and then using the result |z|2= zz.
21. Given that z is a complex number satisfying |2z - 1|=|z2|, prove that |z| = 1 by: (a) letting z = x+iy, (b) squaring the equation and then using the result |z|2= zz.
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:21. Given that z is a complex number satisfying |2z - 1|=|z2|, prove that |z| = 1 by:
(a) letting z = x+iy,
(b) squaring the equation and then using the result |z|2= zz.
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