Let z0 be a fixed complex number. Describe the set of all complex numbers satisfying
(a) | z – z0 | = 2
(b) | z – z0 | = 2i
(c) | z – i| = | z + 1|

Question

Let z0 be a fixed complex number. Describe the set of all complex numbers satisfying
(a) | z – z0 | = 2
(b) | z – z0 | = 2i
(c) | z – i| = | z + 1|

anonymous · Answer

i get that (a) is a Circle, centre z0, radius 2. but i dont get b and c

anonymous · Answer

like if i multiplied both sides by i?

anonymous · Answer

i guess there is no answer to (b) as a length can't be complex

phi · Answer

you mean empty set for (b)

anonymous · Answer

yeah, sorry. But i am still unclear on (c)

phi · Answer

for (3), you can think of i  as 0+1i  and |z - i| is the distance z is from the point 0+1i
this distance must equal the distance z is from the point 1+0i
the locus of points equidistant from 2 points is a line that bisects the line connecting the 2 points

anonymous · Answer

|dw:1347911333511:dw|

anonymous · Answer

the solid line being the solution.

phi · Answer

yes, my picture used +1 oops

anonymous · Answer

kk, thanks for the help tho :)