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If $\alpha$ is the modulus of $z_1=4+3 i$, then a point that does not lie in the region represented by $\left|z-\overline{z_1}\right| \leq \alpha$ is
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The correct answer is:
$\mathrm{z}_1$
Given $z_1=4+3 i$
$\Rightarrow\left|z_1\right|=\alpha=\sqrt{4^2+3^2}=5$
Now, $|z-\overline{4+3 i}| \leq 5 \Rightarrow|z-(4-3 i)| \leq 5$
If we put $\mathrm{z}=4+3 \mathrm{i}$
$|4+3 i-4+3 i|=|6 i| \leq 5$
so $z_1$ is not lies in $\left|z-z_1\right| \leq \alpha$
$\Rightarrow\left|z_1\right|=\alpha=\sqrt{4^2+3^2}=5$
Now, $|z-\overline{4+3 i}| \leq 5 \Rightarrow|z-(4-3 i)| \leq 5$
If we put $\mathrm{z}=4+3 \mathrm{i}$
$|4+3 i-4+3 i|=|6 i| \leq 5$
so $z_1$ is not lies in $\left|z-z_1\right| \leq \alpha$
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