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TS EAMCET · Maths · Complex Number

If A=z=x+iy/real part of z¯-1z-i=2 then the locus of the point Px,y in the Cartesian plane is

  1. A a pair of lines passing through -1,1
  2. B a circle of radius 12 and the centre -12,32
  3. C a pair of lines passing through -1,-2
  4. D a circle of radius 12
Verified Solution

Answer & Solution

Correct Answer

(A) a pair of lines passing through -1,1

Step-by-step Solution

Detailed explanation

Given that Real part of z¯-1z-i = 2 here z = x+iy ⇒z¯ = x-iy ⇒z¯-1z-i = x-iy-1x+iy-i= x-1-iyx+iy-1 ⇒z ¯-1z-i = x-1-iy ×x-iy-1x2+y-12…