If | z 1+ i |=2 , where z =x+ i y, i = -1 represents a circle, then centre ' C ' and radius ' r ' of the circle are

Step-by-step solution

aligned & Given, | z 1+ i | 2, z =x+ i y & | x+ i y 1+ i |=2 & | (x+ i y)(1- i ) (1+ i )(1- i ) |=2 & | x-x i + i y- i ^2 y 1^2-( i )^2 |=2 & | (x+y)+ i (y-x) 2 |=2 & |(x+y)+(y-x) i |=4 & (x+y)^2+(y-x)^2 =4 & (x+y)^2+(y-x)^2=16 aligned aligned & x^2+2 x y+y^2+y^2-2 x y+x^2=16 & 2 x^2+2 y^2=16 & x^2+y^2=8, aligned which is a circle with centre (0,0) and radius is 8 i.e 2 2