14 COMPLEX NUMBERS\ CHAP. 1\ 6. Using the fact that

|z_(1)-z_(2)|

is the distance between two points

z_(1)

and

z_(2)

, give a geometric argument that

|z-1|=|z+i|

represents the line through the origin whose slope is -1 .

6. Using the fact that z1z2 is the distance between two points z1 and z2, give a geometric argument that z1=z+i represents the line through the origin whose slope is -1