# Answer to Question #2831 in Complex Analysis for Waqas

Question #2831
Find the locus of points in the plane satisfying each of the given conditions:
&lt;br&gt;(i) |z-5| = 6 &lt;br&gt; (ii) |z-2i| &gt;=1 &lt;br&gt; (iii) Re(z+2) = -1
&lt;br&gt;(iv) Re{i(conjugate of z)} =3 &lt;br&gt;(v) |z+i| = |z-i|
&lt;br&gt;Also Sketch its diagram.
Please tell me as soon as possible...?
1
2011-05-19T06:55:46-0400
(i) |z-5| = 6
This is a circle of radius 6 with center at 5

(ii) |z-2i| &gt;=1
This is a outer part of a circle of radius 1 with center at 2i together with this circle

(iii) Re(z+2) = -1
This is a vertical line x+2=-1, that is x=3.

(iv) Re{i(conjugate of z)} =3
Let z=x+iy, then
i(conjugate of z) = ix-y,
whence
3 = Re{i(conjugate of z)} =
= Re{-y+ix}= -y
Thus we obtain a horizontal line y=-3.

(v) |z+i| = |z-i|
or any r the set
& |z+i|=r and |z-i|=r
Are two circles of radius r centered at -i and I respectively.
Then |z+i| = |z-i| is the set of all points equidistant to i and &ndash;i
This is a real axis y=0.

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