Let z be a complex number, and c a complex number where |c|=1, show that |1-cz̅|=|c-z|?
I'm struggling with this math question. I tried starting from the fact that |c|=1.
Then the expression becomes
|1-z̅|=|c-z|.
I'm not sure if you can say the same for the c in the right hand side?
If that does work, then
|1-z̅|=|1-z|.
From here, I'm not sure if I could just say that the distance from the origin (which is what the absolute value of a complex number means, yes?) is the same for both z and z̅.
Is my approach correct? I'm not simply asking for a step-by-step answer, I really want to understand this by myself but my professor has not been exactly clear in his lectures.
Thanks.
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|1-z̅|=|c-z| = WTF?!
z=x+jy z^2 = (x^2 - y^2) + 2jxy (a million+j)z = (x-y) + j(x+y) hence, the given equation will become (x^2 - y^2)+(2*(x-y))+2 + j(2xy+2(x+y)) = 0 equating the actual and imaginary areas (x^2 - y^2)+(2*(x-y))+2 = 0 and (2xy+2(x+y)) = 0 (2xy+2(x+y)) = 0 => xy+x+y=0 x(a million+y) = -y x= -y/(a million+y) substitute this in (x^2 - y^2)+(2*(x-y))+2 = 0 U'll get the respond