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The-locus-of-z-given-by-z-1-z-i-1-is-




Question Number 19732 by Tinkutara last updated on 15/Aug/17
The locus of z given by ∣((z − 1)/(z − i))∣ = 1 is
Thelocusofzgivenbyz1zi=1is
Answered by ajfour last updated on 15/Aug/17
z lies on perpendicular bisector  of line joining z=1 and z=i that    passes through origin.  So,    y=x    ((z−z^� )/(2i))=((z+z^� )/2)  or   z−z^� =iz+iz^�   or        (1−i)z−(1+i)z^� =0                multipying by i we get             (1+i)z+(1−i)z^� =0 .
zliesonperpendicularbisectoroflinejoiningz=1andz=ithatpassesthroughorigin.So,y=xzz¯2i=z+z¯2orzz¯=iz+iz¯or(1i)z(1+i)z¯=0multipyingbyiweget(1+i)z+(1i)z¯=0.
Commented by Tinkutara last updated on 15/Aug/17
Thank you very much Sir!
ThankyouverymuchSir!

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