AP EAPCET 2024 - 20th May Evening Shift | Complex Numbers Question 18 | Mathematics

If $z_1=10+6 i, z_2=4+6 i$ and $z$ is any complex number such that the argument of $\frac{\left(z-z_1\right)}{\left(z-z_2\right)}$ is $\frac{\pi}{4}$,

$|z-7-9 i|=3 \sqrt{2}$

$|z-7-9 i|=2 \sqrt{2}$

$|z-3+9 i|=3 \sqrt{2}$

$|z+3-9 i|=2 \sqrt{2}$

AP EAPCET 2024 - 20th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\frac{3-2 i \sin \theta}{1+2 i \sin \theta}$ is purely imaginary number, then $\theta=$

$2 n \pi \pm \frac{\pi}{4}$

$2 n \pi \pm \frac{\pi}{2}$

$n \pi \pm \frac{\pi}{3}$

$n \pi \pm \frac{\pi}{6}$

AP EAPCET 2024 - 20th May Evening Shift

MCQ (Single Correct Answer)

-0

If $z=x+i y, x^2+y^2=1$ and $z_1=z e^{i \theta}$, then $\frac{z_1^{2 n}-1}{z_1^{2 n}+1}=$

$-i \tan \left(n\left(\theta+\tan ^{-1}\left(\frac{y}{x}\right)\right)\right)$

$i \cot \left(n\left(\theta+\tan ^{-1} \frac{y}{x}\right)\right)$

$i \tan \left(n\left(\theta+\tan ^{-1} \frac{x}{u}\right)\right)$

$i \tan \left(n\left(\theta+\tan ^{-1} \frac{y}{x}\right)\right)$

AP EAPCET 2024 - 20th May Morning Shift

MCQ (Single Correct Answer)

-0

If the point $P$ represents the complex number $z=x+i y$ in the argand plane and if $\frac{z+i}{z-i}$ is a purely imaginary number, then the locus of $P$ is

$x^2+y^2+x-y=0$ and $(x, y) \neq(1,0)$

$x^2+y^2-x+y=0$ and $(x, y) \neq(1,0)$

$x^2+y^2-x+y=0$ and $(x, y)=(1,0)$

$x^2+y^2+x+y=0$

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