JEE Main 2022 (Online) 25th June Evening Shift | Complex Numbers Question 71 | Mathematics

Let z₁ and z₂ be two complex numbers such that $${\overline z _1} = i{\overline z _2}$$ and $$\arg \left( {{{{z_1}} \over {{{\overline z }_2}}}} \right) = \pi $$. Then :

$$\arg {z_2} = {\pi \over 4}$$

$$\arg {z_2} = - {{3\pi } \over 4}$$

$$\arg {z_1} = {\pi \over 4}$$

$$\arg {z_1} = - {{3\pi } \over 4}$$

JEE Main 2022 (Online) 25th June Morning Shift

MCQ (Single Correct Answer)

-1

Let a circle C in complex plane pass through the points $${z_1} = 3 + 4i$$, $${z_2} = 4 + 3i$$ and $${z_3} = 5i$$. If $$z( \ne {z_1})$$ is a point on C such that the line through z and z₁ is perpendicular to the line through z₂ and z₃, then $$arg(z)$$ is equal to :

$${\tan ^{ - 1}}\left( {{2 \over {\sqrt 5 }}} \right) - \pi $$

$${\tan ^{ - 1}}\left( {{{24} \over 7}} \right) - \pi $$

$${\tan ^{ - 1}}\left( 3 \right) - \pi $$

$${\tan ^{ - 1}}\left( {{3 \over 4}} \right) - \pi $$

JEE Main 2022 (Online) 24th June Morning Shift

MCQ (Single Correct Answer)

-1

Let $$A = \{ z \in C:1 \le |z - (1 + i)| \le 2\} $$

and $$B = \{ z \in A:|z - (1 - i)| = 1\} $$. Then, B :

is an empty set

contains exactly two elements

contains exactly three elements