Mathematics

Mathematics

Problem

Let O be the origin and A be the point z1=1+2iz_1 = 1 + 2i. If B is the point z2z_2, Re⁡(z2)<0\operatorname{Re}(z_2) < 0, such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT true? [Main July 26, 2022 (I)] (a) arg⁡z2=π−tan⁡−13\arg z_2 = \pi - \tan^{-1} 3 (b) arg⁡(z1−2z2)=−tan⁡−143\arg(z_1 - 2z_2) = -\tan^{-1} \frac{4}{3} (c) ∣z2∣=10|z_2| = \sqrt{10} (d) ∣2z1−z2∣=5|2z_1 - z_2| = 5

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