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 |
|
If \( w \) is a cube root of unity and \((1+w)^7=A+Bw \), the \( A \) and \( B \) are respectively_____
The value of \( \sum_{k=1}^{6}\left( \sin \dfrac{2\pi k}{7}-i \cos \dfrac{2 \pi k}{7} \right)\) is______
Let \(Z_k=\cos \left( \dfrac{3 k \pi}{10} \right)+i \sin \left( \dfrac{2k \pi}{10} \right); k=1,2,…9 \). For each \(Z_k \), there exists a \(Z_j \) such that \( Z_k \cdot Z_j\) is equal to______
Given,
is
root of unity.
Taking, as
, we have
Let \( w \) be the complex number \( \cos \dfrac{2\pi}{3}+i \sin \dfrac{2 \pi}{3}\). Then the number of distinct complex number \( z \) satisfying \( \begin{vmatrix}
z+1 & w &w^2 \\
w & z+w &1 \\
w^2 & 1 & z+w
\end{vmatrix}=0\) is equal to_____
Let
Now,
, the number of
satisfying the given equation is
.
The value of the expression \( 1(2-w)(2-w^2)+2(3-w)(3-w^2)+…+(n-1)(n-w)(n-w^2)\) where, \( w \) is an imaginary cube root of unity is______
The cube roots of unity when represented on the Argand plane form the vertices of an or a _______
Since, cube roots of unity are given by
is an equilateral triangle.
If \( x=a+b, \quad y=a \alpha+b \beta,\quad z=a\beta+b \alpha\), where \(\alpha, \beta \) are complex cube roots of unity, then \( xyz\) is equal to_____
Let
For \(n \in N \), find the value of \( (1-i)^n\left( 1-\dfrac{1}{i} \right)^n\).
Solve: \(\sum_{n=1}^{13}\left( i^n+i^{n+1} \right) \), where \( n \in N \).
If \( \dfrac{(1+i)^2}{2-i}=x+iy\), then find the value of \( x+y \).
If \(\left( \dfrac{1-i}{1+i} \right)^{100}=a+ib \), then find \( (a, b)\).
Hence
If \(a=\cos \theta+i \sin \theta \), find the value of \( \dfrac{1+a}{1-a}\).
If \( (1+i)z=(1-i)\overline {z}\), then \( z \) equals to_______
If \(z=x+iy \), where \( z \overline{z}+2(z+\overline{z})+b=0\), \(b \in R \), represents_____
, which is the equation of a circle.
If \( \dfrac{z-1}{z+1}\) is a purely imaginary number, then find the value of \( |z| (z \neq -1)\)
Since is purely imaginary number then
If \(z_1 \text { and } z_2 \) are two complex numbers such that \( |z_1|=|z_2|\) and \(\arg (z_1) +\arg (z_2)=\pi \), then _____
Let
If if
Now,
If \( |z_1|=1 \text { and } z_2=\dfrac{z_1-1}{z_1+1} (z_1 \neq -1)\) , then \( Re (z_2)\) is_____
If \( z_1, z_2 \text { and } z_3,z_4\) are two pairs of conjugate number, then find \(\arg \left( \dfrac{z_1}{z_4} \right)+\arg \left( \dfrac{z_2}{z_3} \right) \)
Let
Let
The value of \(\sqrt{-25}\times \sqrt{-9} \) is______
Multiplicative inverse of \( 1+i \) is______
Multiplicative inverse of
\( \arg (z)+\arg (\overline{z})\), where \( (\overline{z} \neq 0) \) is_____
Solve:\(\dfrac{(1-i)^3}{1-i^3} \)
The sum of the series \( i+i^2+i^3+…\) up to \(1000\) terms____
up to
terms
For any complex \( z \), the minimum value of \( |z|+|z-1| \) is_______
Let
If , then value of
If \( z \) is a complex number such that \( z \neq 0\) and \( Re (z)=0\), then_____
Let i.e.,
, which is real.