Hi, I did this question today. I did it two ways and then found that I got different answers. I asked my teacher and he couldn't really come up with a reason why.
W=Z* and | Z -3i | = 2 (modulus of (z-3i) =2)
Sketch the locus of W.
My first method was,
Z = U +iV
| U + (V-3)i | = 2
U^2 + (V-3)^2 = 4
and then W is the complex conjigate, giving a circle of
U^2 + (V+3)^2 = 4
My other method was to find the conjigate straight away.
Z = U +iV
| Z + 3i | = | Z* - 3i | (That's easily enough proved given a sheet of papers)
Z* = U -iV
| U + (3-V)i | = 2
U^2 + (3-V)^2 = 4
But surely I've already substituted in for Z* and shouldn't have to reflect it using this method?
If anyone could explain I'd be very grateful. Thank you in advance.
W=Z* and | Z -3i | = 2 (modulus of (z-3i) =2)
Sketch the locus of W.
My first method was,
Z = U +iV
| U + (V-3)i | = 2
U^2 + (V-3)^2 = 4
and then W is the complex conjigate, giving a circle of
U^2 + (V+3)^2 = 4
My other method was to find the conjigate straight away.
Z = U +iV
| Z + 3i | = | Z* - 3i | (That's easily enough proved given a sheet of papers)
Z* = U -iV
| U + (3-V)i | = 2
U^2 + (3-V)^2 = 4
But surely I've already substituted in for Z* and shouldn't have to reflect it using this method?
If anyone could explain I'd be very grateful. Thank you in advance.
