Mathematics 29 Online
OpenStudy (anonymous):

Question here?

OpenStudy (anonymous):

Nothing too difficult now....:-)

OpenStudy (anonymous):

$If z,w \in C so that z ^{2}+w^{2}-2i(z-w)=2$ find z,w

OpenStudy (anonymous):

$z^2+w^2-2i(z-w)=2$ and i take it that w and z are complex right?

OpenStudy (zarkon):

infinitely many solutions

OpenStudy (anonymous):

i think i messed this up once before! hello zarkon!

OpenStudy (zarkon):

hi

OpenStudy (zarkon):

I would write z=a+bi and w=c+di expand ...equate real and imaginary parts...then solve the system

OpenStudy (anonymous):

yes both are complex

OpenStudy (anonymous):

It's a complex difference of squares, myininaya can solve it..:-)

OpenStudy (anonymous):

o.O

OpenStudy (anonymous):

what a lot of algebra. i bet i messed up already

OpenStudy (anonymous):

its easy... do u want me to solve it?

OpenStudy (anonymous):

is there a snap way or do i have to slog through the $a+bi$ stuff?

OpenStudy (anonymous):

no a+bi

OpenStudy (anonymous):

(z-i)2+(w+i)2=0, (z-i)2-i2(w+i)2=0, (z-i)2-(iw-1)2=0, z=i+iw-1 or z=i-iw+1, with w ε C

OpenStudy (anonymous):

$(z-i)2+(w+i)2=0, (z-i)2-i2(w+i)2=0,$ $(z-i)2-(iw-1)2=0,$ $z=i+iw-1 or z=i-iw+1, with w ε C$