The region represented by


The region represented by

$\{z=x+$ iy $\in C:|z|-\operatorname{Re}(z) \leq 1\}$ is also given by the inequality :


  1. $y^{2} \geq x+1$

  2. $\mathrm{y}^{2} \geq 2(\mathrm{x}+1)$

  3. $y^{2} \leq x+\frac{1}{2}$

  4. $y^{2} \leq 2\left(x+\frac{1}{2}\right)$

Correct Option: , 4



$|\mathrm{z}|-\mathrm{ke}(\mathrm{z}) \leq 1$

$\Rightarrow \sqrt{x^{2}+y^{2}}-x \leq 1$

$\Rightarrow \sqrt{x^{2}+y^{2}} \leq 1+x$

$\Rightarrow x^{2}+y^{2} \leq 1+2 x+x^{2}$

$\Rightarrow y^{2} \leq 2 x+1$

$\Rightarrow y^{2} \leq 2\left(x+\frac{1}{2}\right)$

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