Question 1 :
Two complex numbers are represented by ordered pairs $z_1: (a,b)\ \&\ z_2: (c,d)$, when these two complex numbers are equal?
Question 3 :
The value of $\left(i^{18} + \left(\dfrac{1}{i} ^{25}\right) \right)^3$ is equal to
Question 4 :
Let $z_1$ and $z_2$ be complex numbers, then $|z_1 + z_2|^2 + |z_1 - z_2|^2$ is equal to
Question 5 :
If $i^2$ $= -1$, then find the odd one out of the following expressions.
Question 6 :
A complex number is represented by an ordered pair $(a,b)$, which of the following is true for $a$ and $b$?
Question 7 :
If the discriminant of a quadratic equation is negative, then its roots are:
Question 9 :
Inequality $a + i b > c + i d$ can be explained only when :
Question 10 :
Determine the nature of roots of the equation $x^2 + 2x\sqrt{3}+3=0$.<br>
Question 11 :
<span>Find the value of $k$ for the following quadratic equation, so that they have two real and equal roots:</span><div>$kx^2 - 2 \sqrt 5x + 4 = 0$</div>
Question 12 :
If $a, b, c$ are real and $b^2- 4ac $ is perfect square then the roots of the equation $ax^2+bx+c=0$, will be:
Question 14 :
In the complex plane, what is the distance of $4-2i$ from the origin?
Question 15 :
if $ 2 +(2a + 5ib) = 8 + 10 i $ then
Question 16 :
Let $z$ and $\omega $ are two non -zero complex number such that $|z|=|\omega|$ and arg$z+arg \omega =\pi$. then $z$ equal to ?<br/>
Question 18 :
The number of complex numbers $z$ such that $|z+1|=|z-3|$ equals :-
Question 21 :
The roots of the equation ${ \left( z+\alpha \beta \right) }^{ 3 }={ \alpha }^{ 3 }$ represent the vertices of a triangle, one of whose sides is of length
Question 22 :
Mark against the correct answer in each of the following .<br>$i^{124}=$?
Question 24 :
If $z = 1 + i$, then the multiplicative inverse of $z^2$ is (where $i = \sqrt{-1}$)
Question 25 :
If $z$ is a complex number such that $|z|=1$, then $\left|\dfrac 1{\bar z}\right|$ is
Question 26 :
For any complex number $z$, the minimum value of $\left| z \right| +\left| z-1 \right| $ is
Question 27 :
If the conjugate of (x + iy) (1- 2i) be 1 + i then x and y are
Question 29 :
The maximum value of $\left| {{\rm{3z + 9 - 7i}}\left| {{\rm{if}}} \right|{\rm{z + 2 - i}}\left. {} \right|} \right.{\rm{ = 5}}$is
Question 30 :
$\displaystyle \frac{3+2i sin \theta}{1-2 i sin \theta}$ will be purely imaginary, if $\theta$ =
Question 31 :
If $z=x+iy(x,y\epsilon R,x\neq -1/2),$ the number of values of z satisfying $\left | z \right |^{n}=z^{2}\left | z \right |^{n-2}+1.(n\epsilon N,n> 1)$is
Question 36 :
If $\cos { \left( \log { { i }^{ 4i } } \right) } =a+ib$, then
Question 38 :
Mark against the correct answer in each of the following .<br>$i^{-38}=$?
Question 39 :
The argument of $\displaystyle \frac{(1 - i \sqrt 3)}{(1 + i \sqrt 3)}$ is
Question 40 :
Total number of complex numbers $z$, satisfying $Re({z}^{2})=0,{ \left| z \right| }=\sqrt{3}$, is equal to
Question 41 :
Solve $\displaystyle \left ( 1-i \right )x+\left ( 1+i \right )y= 1-3i,$
Question 42 :
What is the modulus of $\cfrac { \sqrt { 2 } +i }{ \sqrt { 2 } -i } $ where $i=\sqrt { -1 } $
Question 44 :
If the discriminant of the equation $3x^{2} - 4x + k = 0$ is $64$, then $k =$ _________.
Question 47 :
<span>Find the modulus and the principal value of the argument of the number $1-i$</span>
Question 49 :
If the roots of $2x^2+3x+p=0$ be equal, then the value of p is :