Let be a complex number satisfying

MATHEMATICS · Subjective · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

Let zz be a complex number satisfying ∣z−3−4i∣=α|z-3-4i|=\alpha. Let zaz_a and zbz_b be the corresponding complex numbers for which ∣z+2+2i∣|z+2+2i| is minimum and maximum, respectively. Find the integral values of α\alpha satisfying arg⁡(za+2+2izb−3−4i)=π4.\arg\left(\frac{z_a+2+2i}{z_b-3-4i}\right)=\frac{\pi}{4}.

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