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← JEE Main 2022 · 26 Jul · Shift 1
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JEE Main 2022 · 26 Jul · Shift 1, Mathematics question 2

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 ?

Choose one option
Answer and worked solution

Official answer: D

B. Right angle at A, AB=OAAB=OA: z2=z1+iz1=−1+3iz_2=z_1+iz_1=-1+3i (Re < 0).

Check. ∣z2∣=10|z_2|=\sqrt{10}, arg⁡z2=π−tan⁡−13\arg z_2=\pi-\tan^{-1}3, z1−2z2=3−4iz_1-2z_2=3-4i (argument −tan⁡−143-\tan^{-1}\frac43), but ∣2z1−z2∣=∣3+i∣=10≠5|2z_1-z_2|=|3+i|=\sqrt{10}\ne5.

(D)

Topics:Geometry in the complex planeModulus and argument
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