If the real part of z +2 z -1 is 4, z 1, then the locus of the point representing z in the complex plane is

Step-by-step solution

Real part of z +2 z -1 is given by array l 1 2 [ z +2 z -1 + ( z +2 z -1 ) ]=4 z +2 z -1 + z+2 z-1 =8 z z - z +2 z-2+z z +2 z -z-2 =8(z z - z -z+1) z z - 3 2 z- 3 2 z +2=0 array Comparing with the equation z z + a z+a z +b=0, we get a=- 3 2 and b=2 . Thus, the locus of z given by the equation (i) is a circle with centre = 1 2