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Complex Numbers question

2022 · 26 Jul · Shift 1 · Q26

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PYQ Library
JEE Main
Mathematics
Complex Numbers
2022 · 26 Jul · Shift 1 · Q26

Complex Numbers question

2022 · 26 Jul · Shift 1 · Q26

JEE MainMathematicsComplex NumbersMCQ+4 / −1

Let O be the origin and A be the point

{z_1} = 1 + 2i

. If B is the point

{z_2}

,

{\mathop{\rm Re} olimits} ({z_2}) \lt 0

, such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT true?

A
$\arg {z_2} = \pi - {\tan ^{ - 1}}3$
B
$\arg ({z_1} - 2{z_2}) = - {\tan ^{ - 1}}{4 \over 3}$
C
$|{z_2}| = \sqrt {10}$
D
$|2{z_1} - {z_2}| = 5$

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