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

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

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

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Analyzing +4 | -1

Let a circle

C

in complex plane pass through the points

{z_1} = 3 + 4i,\,\,{z_2} = 4 + 3i

and

\,{z_3} = 5i.\,

z( \ne {z_1})

sis point on

C

such that the line through

z

and

{z_1}

is perpendicular to the line through

{z_2}

and

{z_3}

then

\arg (z)

is equal to:

View answer and explanation

Correct option: B

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

The correct answer is B (

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

) because it is the argument of the point z on the circle, calculated using the given conditions and complex number properties.