Locate the points representing the complex number z on the Argand plane.
(a) `|z+1-2i|=2sqrt2`
(b) `|z-1|^(2)+|z+1|^(2)=4`
(c) `|(z-2008)/(z+2008)|=2007`
(d) |z-2008|= |z- 2007i|
( e) |z-2008|+|z + 2008| = 4018

Explanation

(a) The complex number z lies on the cirumference of the circle centred at (-1,2) and whose radius = ` 2sqrt2`
(b) Let z= z + iy , then the given condition reduces to
`(x -1)^(2) + y^(2) + (x +1)^(2)+y^(2) =4`
` Rightarrow x^(2) + y^(2) =1`
The complex number z lies on the circumference of the unit circle with centred at the origin.
(c) we have , `|(z-2008)/( z+ 2008)| = 2007`
` Rightarrow (x-2008)^(2) +y^(2) = (2007)^(2) [( x + 2008)^(2) + y^(2)]`
which represents a circle.
(d) |Z-2008|=|z-2007i|
`Rightarrow x^(2)-4016x+y^(2)+ (2008)^(2)=x^(2)+y^(2)-4014y + (2007)^(2)`
`Rightarrow 4016x -4014y= (2008)^(2)-(2007)^(2) = 4015`
Which represents a striaght line.
(e) The equation |z-2008| + |z + 2008| = 4018 represents an ellipse with foci at ( 2008,0) and ( -2008 ,0)