[JEE Advanced 1981] define z 1 preceq z 2 iff x 1 x 2 and y 1
Define $z_1\preceq z_2$ iff $x_1\le x_2$ and $y_1\le y_2$. For all $z$ with $1\preceq z$, is $\dfrac{1-z}{1+z}\preceq0$?
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· 4d ago
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Answer: True.
For $\operatorname{Re}z\ge1,\operatorname{Im}z\ge0$, $\operatorname{Re}\frac{1-z}{1+z}=\frac{1-|z|^2}{|1+z|^2}\le0$ and $\operatorname{Im}=\frac{-2\,\operatorname{Im}z}{|1+z|^2}\le0$, so $\frac{1-z}{1+z}\preceq0$.
JEE Advanced 1981 · Complex Numbers — verified solution by the Vidaara Team.
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