Question

If Z is a complex number satisfying the realation |Z+1| = Z+2(1+i) then Z is

Answer 1

Answer:

solved

Step-by-step explanation:

z = x+iy = (x,y)

|Z+1| = Z+2(1+i)

|x+1+iy| = x+iy+2+2i

 |x+1+iy| = x+2 +i(y+2)

( x+1 )²  + y² = (x+2)² - (y+2)² +2i(x+2)(y+2)

-2x-3 -4y-4 = 2i(x+2)(y+2)

x+2y-7/2 + i(x+2)(y+2) = 0

x = y = -2

z = (-2,-2) & ALL the points satisfying the line x+2y-7/2 = 0