Interpret this c.n question.. (1 Viewer)

[underthesun]

there's this strange question from the past 4unit CSSA for complex numbers,

The complex number z satisfies both :

|z - 1| =< |z-i|

and

|z - 2 - 2i| =< 1

In an argand diagram indicate the region which contains the point P representing z.

(I highlighted this region in orange, or am I wrong?)

if P moves on the boundary of this region and arg(z-1) = (pi/4), find the value of z in the form x+iy where x and y are real.

As you can see, there's two point of intersection with arg(z-1) = pi/4, and the region's outline, and arg(z-1) = pi/4 is the blue line.

Hints anybody?

 

[aspect]

if you are looking for the points, get the cartesian equations of the 2 curves and solve them for x and y



i.e. in this :

try solving these simultaneously

(x-2)^2+(y-2)^2=1
and

y=x-1

 

[Rahul]

Originally posted by aspect

(x-2)^2+(y-2)^2=1
and

y=x-1

dont u mean y = x ? not y = x-1

i got the other equation same as u

 

[aspect]

arg(z-1)=pi/4 means the line is slanted at 45 degrees and passing throught the point (1,0)

 

[underthesun]

In that case I found two values, at x=2 and x=3. But it was asking for one z value.. so, what do you think?

 

[ND]

z = x + iy so find the y values and sub in.

edit: sorry, misread your post. One z value? that is not possible.

 

[underthesun]

oh well.. blame CSSA then.

 

[aspect]

probably a question where u are supposed to list both and if you dont you lose a mark..