If satisfies the inequality

MATHEMATICS · Single correct · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

If zz satisfies the inequality ∣z−1∣<∣z+1∣|z - 1| < |z + 1| , then one has (1) ∣z−2−i∣<∣z+2−i∣,i=−1|z - 2 - i| < |z + 2 - i|, i = \sqrt{-1} (2) ∣arg⁡(z+i)∣<π2,i=−1|\arg(z + i)| < \frac{\pi}{2}, i = \sqrt{-1} (3) Re⁡(z)<0\operatorname{Re}(z) < 0 (4) Im⁡(izˉ)>0,i=−1\operatorname{Im}(i\bar{z}) > 0, i = \sqrt{-1}

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