Choose the Correct options
0 of 25 questions completed
Questions:
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading…
You must sign in or sign up to start the quiz.
You must first complete the following:
0 of 25 questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 point(s), (0)
Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)
Average score 

Your score 

The value of \(\sum_{n=1}^{13}\left( i^n+i^{n+1} \right)\), is equals to______
If \(\begin{vmatrix}
6i & 3i & 1 \\
4& 3i &1 \\
20 & 3 & i
\end{vmatrix}=x+iy \), then_____
The smallest positive integer \( n \) for which \( \left( \dfrac{1+i}{1i} \right)^n=1\) is______
The smallest positive integer for which is .
A complex number \( Z \) is said to be unimodular, if \( Z \neq 1 \). If \(Z_1 \text { and } Z_2 \) are complex number such that \(\dfrac{Z_12Z_2}{2Z_1Z_2} \) is unimodular and \( Z_2\) is not unimodular, then the points \( Z_1\) lies on a_____
is not unimodular i.e., and is unimodular.
Point lies on a circle of radius .
If \( Z \) is a complex number such that \( Z \geq 2 \), then the minimum value of \( Z+\dfrac{1}{2} \).
is the region on or outside circle whose center is and radius is . Minimum is distance of , which lies on circle from .
Minimum distance of from
Hence, minimum value of lies in the interval .
Let \( z \) be a complex number such that the imaginary part of \( z \) is nonzero and \( a=z^2+z+1\) is real. Then, \( a \) cannot take the value______
For do not have real roots , < <
So, other 3 options are showing imaginary roots.
Let \( z=x+iy \), be a complex number where, \( x \text { and } y \) are integers. Then, the area of the rectangle whose vertices are the root of the equation \( z \overline{z}^3+\overline{z}z^3=350\).
Hence
Area of rectangle
If \( z=1 \) and \( z \neq \pm 1\), then all the values of \(\dfrac{z}{1z^2}\) lie on ______
Hence , lies on the imaginary axis i.e. yaxis.
If \( w=\alpha+i \beta\), where \(\beta \neq 0\) and \( z \neq 1 \) satisfies the condition that \( \left( \dfrac{w\overline{w}z}{1z} \right)\) is purely real, then the set of values of \( z \) is_____
be purely real.
If \( z=1 \) and \( \dfrac{z1}{z+1}( \text { where } z \neq 1)\) then \( Re(w) \) is______
and
For all complex numbers \( z_1, z_2 \) satisfying \( z_1=12\) and \( z_234i=5 \), the minimum value of \( z_1z_2\) is_____
The minimum value of is .
If \( z_1, z_2 \text { and } z_3 \) are complex numbers such that \(z_1=z_2=z_3=\left \dfrac{1}{z_1}+\dfrac{1}{z_2}+\dfrac{1}{z_3} \right=1 \) then \( z_1+z_2+z_3 \) is_____
Similarly,
Again,
For positive integers \( n_1, n_2\) the value of expression \( (1+i)^n+(1+i^3)^{n_1}+(1+i^5)^{n_2}+(1+i^7)^{n_2}\) here \(i=\sqrt{1} \) is a real number , iff_____
This is a real number irrespective of the values > 0 and > 0.
The complex numbers \( \sin x + i \cos 2x \) and \(\cos x i \sin 2x \) are conjugate to each other, for_____
Since,
which is not possible at the same time.
Hence, no solution exists.
The points \( z_1, z_2, z_3 \text { and } z_4\) in the complex plane are the vertices of parallelogram taken in order , iff_____
Midpoint of midpoint of .
If \( z=x+iy \) and \( w=\left( \dfrac{1iz}{zi} \right)\) then \( w=1\) implies that in the complex plane.
It is a perpendicular bisector of and , i.e., xaxis. Thus, lies on the real axis.
The inequality \(z4 \) < \(z2 \) represents the region given by_____
<
Since , > represents the region on right side of the perpendicular bisector of and .
>
> and
If \(z= \left( \dfrac{\sqrt{3}}{2}+\dfrac{i}{2} \right)^5+\left( \dfrac{\sqrt{3}}{2}\dfrac{i}{2} \right)^5 \) then ______
Now
and
< and
The complex numbers \(z=x+iy \) which satisfy the equation \( \left \dfrac{z5i}{z+5i} \right=1\), lies on_______
Given,
Perpendicualr bisector of and is xaxis.
Let \(z_1 \text { and }z_2 \) be complex numbers such that \(z_1 \neq z_2 \text { and } z_1 =z_2 \). If \( z_1\) has positive real part and \(z_2 \) has negative imaginary part, then \( \dfrac{z_1+z_2}{z_1z_2}\) may be______
Now,
As,
Which is purely imaginary.
If \( z=a+ib\) and \( z_2=c+id\) are complex numbers such that \(z_1=z_2=1 \) and \( Re(z_1\overline{z_2})=0\), then the pair of complex numbers \( w_1=a+ic\) and \( w_2=b+id\) satisfies, _____
Also,
Given,
Let \(A, B ,C \) are three sets of complex number as defined below:
\( A=\left\{ z: Im~ z \geq 1 \right\}, \quad B=\left\{ z: z2i=3 \right\}, \quad C=\left\{ z: Re(1i)z=\sqrt{2} \right\}\),
then find \(\text { min } z \in S \) \( 13iz\) is equal to_____
perpendicular distance of point from the line
Let \( z \) be any point in \( A\cap B\cap C\) and let \( w \) be any point satisfying \( w2i \leq 3\) then \( zw+3\) lies between_______
Since, <
<
< <
< <
Also,
< <
\( S=S_1\cap S_2\cap S_3\), where \(S_1= z \in C: z \) 0 \right\}[/latex] and \(S_3=\left\{ z \in C : Re z > 0 \right\}\), where \( z \) be any point in \( A\cap B \cap C\), then \(z+1i^2+z5i^2 \) lies between______
< <
The set of points \( z \) satisfying \( ziz=z+iz\) is contained in or equal to_____
is equidistance from the points and whose perpendicular bisector is