Complex Numbers · Mathematics · AP EAPCET

Start Practice

MCQ (Single Correct Answer)

1
The complex conjugate of $(4-3 i)(2+3 i)(1+4 i)$ is.
AP EAPCET 2024 - 21th May Morning Shift
2
If the amplitude of $(z-2)$ is $\frac{\pi}{2}$, then the locus of $z$ is
AP EAPCET 2024 - 21th May Morning Shift
3
If $\omega$ is the cube root of unity, $$ \frac{a+b \omega+c \omega^2}{c+a \omega+b \omega^2}+\frac{a+b \omega+c \omega^2}{b+c \omega+b \omega^2}= $$
AP EAPCET 2024 - 21th May Morning Shift
4
If $(3+i)$ is a root of $x^2+a x+b=0$, then $a=$
AP EAPCET 2024 - 21th May Morning Shift
5
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 $\frac{\pi}{4}$,
AP EAPCET 2024 - 20th May Evening Shift
6
If $\frac{3-2 i \sin \theta}{1+2 i \sin \theta}$ is purely imaginary number, then $\theta=$
AP EAPCET 2024 - 20th May Evening Shift
7
If $z=x+i y, x^2+y^2=1$ and $z_1=z e^{i \theta}$, then $\frac{z_1^{2 n}-1}{z_1^{2 n}+1}=$
AP EAPCET 2024 - 20th May Evening Shift
8
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
AP EAPCET 2024 - 20th May Morning Shift
9
$S=\{z \in C /|z+1-i|=1\}$ represents
AP EAPCET 2024 - 20th May Morning Shift
10
If $m, n$ are respectively the least positive and greatest negative integer value of $k$ such that $\left(\frac{1-i}{1+i}\right)^k=-i$, then $m-n=$
AP EAPCET 2024 - 19th May Evening Shift
11
If a complex number $z$ is such that $\frac{z-2 i}{z-2}$ is purely imaginary number and the locus of $z$ is a closed curve, then the area of the region bounded by that closed curve and lying in the first quadrant is $\frac{z-2 i}{z-2}$
AP EAPCET 2024 - 19th May Evening Shift
12
Real part of $\frac{(\cos a+i \sin a)^6}{(\sin b+i \cos b)^8}$ is
AP EAPCET 2024 - 19th May Evening Shift
13
If real parts of $\sqrt{-5-12 i}, \sqrt{5+12 i}$ are positive values, the real part of $\sqrt{-8-6 i}$ is a negative value and $a+i b=\frac{\sqrt{-5-12 i}+\sqrt{5+12 i}}{\sqrt{-8-6 i}}$, then $2 a+b=$
AP EAPCET 2024 - 18th May Morning Shift
14
The set of all real values of $ c $ for which the equation $ z\overline{z} + (4 - 3i)z + (4 + 3i)\overline{z} + c = 0 $ represents a circle, is
AP EAPCET 2024 - 18th May Morning Shift
15
If $ z = x + iy $ is a complex number, then the number of distinct solutions of the equation $ z^3 + \overline{z} = 0 $ is
AP EAPCET 2024 - 18th May Morning Shift
16

By simplifying $$i^{18}-3 i^7+i^2\left(1+i^4\right)(i)^{22}$$, we get

AP EAPCET 2022 - 5th July Morning Shift
17

The values of $$x$$ for which $$\sin x+i \cos 2 x$$ and $$\cos x-i \sin 2 x$$ are conjugate to each other are

AP EAPCET 2022 - 5th July Morning Shift
18

The locus of a point $$z$$ satisfying $$|z|^2=\operatorname{Re}(z)$$ is a circle with centre

AP EAPCET 2022 - 5th July Morning Shift
19

Multiplicative inverse of the complex number $$(\sin \theta, \cos \theta)$$ is

AP EAPCET 2022 - 4th July Evening Shift
20

$$\sum_\limits{k=0}^{440} i^k=x+i y \Rightarrow x^{100}+x^{99} y+x^{242} y^2+x^{97} y^3=$$

AP EAPCET 2022 - 4th July Evening Shift
21

If $$e^{i \theta}=\operatorname{cis} \theta$$, then $$\sum_\limits{n=0}^{\infty} \frac{\cos (n \theta)}{2^n}=$$

AP EAPCET 2022 - 4th July Evening Shift
22

$$i z^3+z^2-z+i=0 \Rightarrow|z|=$$

AP EAPCET 2022 - 4th July Morning Shift
23

If $$\frac{x-1}{3+i}+\frac{y-1}{3-i}=i$$, then the true statement among the following is

AP EAPCET 2022 - 4th July Morning Shift
24

The number of integer solutions of the equation $$|1-i|^x=2^x$$ is

AP EAPCET 2022 - 4th July Morning Shift
25

If $$z_1=2+3 i$$ and $$z_2=3+2 i$$, where $$i=\sqrt{-1}$$, then $$\left[\begin{array}{cc}z_1 & z_2 \\ -\bar{z}_2 & \bar{z}_1\end{array}\right]\left[\begin{array}{cc}\bar{z}_1 & -z_2 \\ \bar{z}_2 & z_1\end{array}\right]$$ is equal to

AP EAPCET 2021 - 20th August Morning Shift
26

The radius of the circle represented by $$(1+i)(1+3i)(1+7i)=x+iy$$ is $$(i=\sqrt{-1})$$.

AP EAPCET 2021 - 20th August Morning Shift
27

If $$1, \alpha_1, \alpha_2, \alpha_3$$ and $$\alpha_4$$ are the roots of $$z^5-1=0$$ and $$\omega$$ is a cube root of units, then $$(\omega-1)\left(\omega-\alpha_1\right)\left(\omega-\alpha_2\right)\left(\omega-\alpha_3\right)\left(\omega-\alpha_4\right)+\omega$$ is equal to

AP EAPCET 2021 - 20th August Morning Shift
28

If $$a > 0$$ and $$z=x+i y$$, then $$\log _{\cos ^2 \theta}|z-a|>\log _{\cos ^2 \theta}|z-a i|,(\theta \in R)$$ implies

AP EAPCET 2021 - 20th August Morning Shift
29

If one root of the equation $$i x^2-2(i+1) x+(2-i)=0$$ is $$(2-i)$$, then the other root is

AP EAPCET 2021 - 20th August Morning Shift
30

If $$|z-2|=|z-1|$$, where $$z$$ is a complex number, then locus $$z$$ is a straight line

AP EAPCET 2021 - 19th August Evening Shift
31

If $${\left( {{{1 + i} \over {1 - i}}} \right)^m} = 1$$, then m cannot be equal to

AP EAPCET 2021 - 19th August Evening Shift
32

$$(\sin \theta-i \cos \theta)^3$$ is equal to

AP EAPCET 2021 - 19th August Morning Shift
33

Real part of $$(\cos 4+i \sin 4+1)^{2020}$$ is

AP EAPCET 2021 - 19th August Morning Shift
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12