Let and be two complex numbers represented by points on circles and respectively

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

Problem

Let z1z_1 and z2z_2 be two complex numbers represented by points on circles ∣z∣=1|z| = 1 and ∣z∣=2|z| = 2 respectively, then max. ∣2z1+z2∣=4|2z_1 + z_2| = 4 min. ∣z1−z2∣=1|z_1 - z_2| = 1 (1) max. ∣2z1+z2∣=4|2z_1 + z_2| = 4 (2) min. ∣z1−z2∣=1|z_1 - z_2| = 1 (3) ∣z2+1z1∣≤3| z_2 + \frac{1}{z_1} | \le 3 (4) ∣z1+2z2∣≤2| z_1 + \frac{2}{z_2} | \le 2

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