If P(x, y) denotes z=x+i y in Argand's plane and | z-1 z+2 i |=1 , then the locus of P is a/an

Step-by-step solution

Given, z=x+i y and | z-1 z+2 i |=1 | (x+i y)-1 (x+i y)+2 i |=1 |(x-1)+i y|=|x+(y+2) i| Squaring on both sides, |(x-1)+i y|²=|x+(y+2) i|² (x-1)²+y²=x²+(y+2)² x²+y²+1-2 x=x²+y²+4+4 y 2 x+24+3=0 , which represents a straight line.