Let and be complex numbers

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

Problem

Let zz and ω\omega be complex numbers. If Re(z)=∣z−2∣\text{Re}(z) = |z-2|, Re(ω)=∣ω−2∣\text{Re}(\omega) = |\omega-2| and arg⁡(z−ω)=π3\arg(z-\omega) = \frac{\pi}{3}, the value of Im(z+ω)\text{Im}(z+\omega) is (1) 13\frac{1}{\sqrt{3}} (2) 23\frac{2}{\sqrt{3}} (3) 3\sqrt{3} (4) 43\frac{4}{\sqrt{3}}

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