Complex Numbers PYQs - Last 5 Years

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All Complex Numbers PYQs Last 10 Years Create chapter test

Practice 91 AP EAPCET Mathematics questions from Complex Numbers. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 5 Years Complex Numbers Questions

Showing 41 of 91 filtered questions.

1Complex Numbers

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

2Complex Numbers

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

3Complex Numbers

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

4Complex Numbers

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 $\frac{\pi}{4}$,

5Complex Numbers

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 $\frac{z-2 i}{z-2}$

6Complex Numbers

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 $m-n=$

7Complex Numbers

Real part of $\frac{(\cos a+i \sin a)^6}{(\sin b+i \cos b)^8}$ is

8Complex Numbers

If $ z = x + iy $ is a complex number, then the number of distinct solutions of the equation $ z^3 + \overline{z} = 0 $ is

9Complex Numbers

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

10Complex Numbers

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 $2 a+b=$

11Complex Numbers

$(1+i)^{2024}+(1-i)^{2024}=$

12Complex Numbers

The number of all possible solutions of the equation $z^3+\bar{z}=0$ is

13Complex Numbers

If $z_1=(2,-1)$ and $z_2=(6,3)$, then $\operatorname{amp}\left(\frac{z_1-z_2}{z_1+z_2}\right)=$

14Complex Numbers

$\left[\sqrt{2}\left(\cos 56^{\circ} 15^{\prime}+i \sin 56^{\circ} 15^{\prime}\right)\right]^8=$

15Complex Numbers

The product of the four values of $(1+i \sqrt{3})^{3 / 4}$ is

16Complex Numbers

One of the 15 th roots of -1 is

17Complex Numbers

If $\left|z-\frac{2}{z}\right|=2$, then the greatest value of $|z|$ is

18Complex Numbers

\(S=\{z \in C /|z-1+i|=1\} \text { represents }\)

19Complex Numbers

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

20Complex Numbers

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

21Complex Numbers

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

22Complex Numbers

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

23Complex Numbers

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

24Complex Numbers

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

25Complex Numbers

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

26Complex Numbers

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

27Complex Numbers

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

28Complex Numbers

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

29Complex Numbers

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

30Complex Numbers

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-\...

31Complex Numbers

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

32Complex Numbers

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

33Complex Numbers

\(\left(\frac{\sqrt{6}-\sqrt{2}}{4}+\frac{\sqrt{6}+\sqrt{2}}{4} i\right)^{2020}\) is equal to

34Complex Numbers

What is the value of \((1-i \sqrt{3})^9\) is equal to

35Complex Numbers

A real value of \(x\) will satisfy the equation, \(\left(\frac{3-4 i x}{3+4 i x}\right)=\alpha-i \beta,(\alpha, \beta\) are real \()\), if

36Complex Numbers

If \(\left|z_1+z_2\right|^2=\left|z_1\right|^2+\left|z_2\right|^2\), where \(z_1\) and \(z_2\) are two complex numbers, then

37Complex Numbers

Let \(Z_1, Z_2\) and \(Z_3\) be three non zero complex numbers such that \(a=\left|Z_1\right|, b=\left|Z_2\right|\) and \(c=\left|Z_3\right|\), if the determinant $$\left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\righ...

38Complex Numbers

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

39Complex Numbers

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

40Complex Numbers

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

41Complex Numbers

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