Hey I need some help with these complex numbers questions. I can pay the little fg that I have for help

Shade each region in the complex plane. Justify your solution.

a) |z-6-2i| <2

b ) z - Conjugate[z] = 4

c) 1+z, where |z|=1

This post was edited by Bloo_Guardian on Jan 18 2014 07:02pm

with the standard metric those questions are not difficult, just take it as a plane with the x-axis real and the y-axis imaginary

a) is the interior of the circle with radius 2 around the pont -6-2i
does not exist since z minus it's conjugate is two times the imaginary part of the number - or is the absolute value requested?
c) unit circle around the point 1+0i

for b this is what I did

Let z = x + iy and Conjugate[z] = x - iy
I'll just call Conjugate[z] zbar from now on

z - zbar = 4
x + iy - (x - iy) = 4
2iy = 4
iy = 2 multiply both sides by i
y = -2i

So given y = -2i what region would I shade? Or is there something wrong with how I'm approaching it?

Also for c this is what I have so far..

Let z = x + iy
|z| = 1 therefore x + iy = (x,y)*1/|x^2+y^2|

and I don't know where to go from there ...

This post was edited by Bloo_Guardian on Jan 18 2014 08:49pm

pretty sure y cannot include i if it's in the form x + yi.
y has to be a real number

/edit: not clear how you got this either:



/edit2: oh yeah. derp.

This post was edited by carteblanche on Jan 18 2014 08:53pm

Woops just edited that, I multiplied both sides by i

and you're right what the hell am I doing

This post was edited by Bloo_Guardian on Jan 18 2014 08:50pm

Okay for c I think I get it. |z|=1 just means the unit circle but aren't disks in the complex region given as |z-a| < r where a is the centre of the circle and r is the radius.
In this case the radius is 1.
But since it is saying 1+z which is the same as z+1 which in the form of z-a would be z-(-1) so wouldn't it be the unit circle around -1+0i ?

for b, you got y=-2i
so, shade a horizontal line , y=-2

This post was edited by saber_x3 on Jan 18 2014 09:05pm

you are correct till 2iy=4 but afterwards you get confused
as said, if you are asked for z-zconjugate=4 there is no solution
but if the question is abs(z-zconjugate)=4 then all numbers with imaginary part plus or minus two are the solution, ie two lines



while your reasoning is correct, you are not asked for the solution of abs(1+z) but 1+abs(z), think about it