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Question 3. Let p, q E C be fixed complex numbers. Show the the equation |zp|=|zq| is equivalent to the equation Re (zp-q) = |p|² – 1q|² 2 (Hint: square both sides of the first equation). (Remkark: since the locus of the second equation is a straight line, this gives an alternative proof that the locus of the first equation is a straight line).

Question 3. Let p, q E C be fixed complex numbers. Show the the equation |zp|=|zq| is equivalent to the equation Re (zp-q) = |p|² – 1q|² 2 (Hint: square both sides of the first equation). (Remkark: since the locus of the second equation is a straight line, this gives an alternative proof that the locus of the first equation is a straight line).

Advanced Engineering Mathematics
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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Question 3. Let p, q E C be fixed complex numbers. Show the the equation |zp|=|zq|l is equivalent to the equation |p|² - 191² 2 Re (zp-q) (Hint: square both sides of the first equation). (Remkark: since the locus of the second equation is a straight line, this gives an alternative proof that the locus of the first equation is a straight line). =
Transcribed Image Text:Question 3. Let p, q E C be fixed complex numbers. Show the the equation |zp|=|zq|l is equivalent to the equation |p|² - 191² 2 Re (zp-q) (Hint: square both sides of the first equation). (Remkark: since the locus of the second equation is a straight line, this gives an alternative proof that the locus of the first equation is a straight line). =
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