Quick question (1 Viewer)

[NubMuncher]

I think the answers in my resource book is wrong ...

What is the locus of Re(z-1/c)=0 where c is the conjugate of z.

=> x^2 + y^2 = 1 ??

 

[Bored Of Fail1]

its easy

 

[NubMuncher]

Yeah my textbook has a different answer though :S

 

[khorne]

Umm...Haven't done complex in a while, but...

Re(z-1/z*) = 0

so basically, z* = x-iy so multiply by x+iy

so Re((x+iy-1)(x+iy)/(x^2 + y^2)) = 0

so x^2-y^2-x/(x^2+y^2) = 0 when taking the real part as the expansion is x^2 +2iyx -y^2 -x -iy, i.e re of that is x^2 -y^2 -x...

Again, might be wrong but still

 

[shaon0]

x=0 or z=+-1 could also be soln's i think. It's been a while since complex no's so i could be wrong.

 

[deterministic]

I think the answers in my resource book is wrong ...

What is the locus of Re(z-1/c)=0 where c is the conjugate of z.

=> x^2 + y^2 = 1 ??

Do you mean
or

 

[deterministic]

For the former:
Let z=x+iy


Taking real parts we get:

hence either x=0 or

 

[deterministic]

For the later:

Hence: