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Class 11 Maths
Complex Numbers And Quadratic Equations
Quiz 2
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The multiplicative inverse of $(2 + \sqrt {3} i)^2$ is
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$ \frac {1}{49} + \frac {4 \sqrt 3}{49} i$
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$ \frac {1}{49} - \frac {4 \sqrt 3}{49} i$
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$ \frac {1}{49} + \frac { \sqrt 3}{49} i$
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$ \frac {1}{48} + \frac { \sqrt 3}{12} i$
The conjugate of $ \frac { 2-i}{(1 -2i)^2}$ is
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$ \frac {-2}{25} – i \frac {11}{25}$
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$ \frac {-2}{25} + i \frac {11}{25}$
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$ \frac {-2}{5} – i \frac {11}{5}$
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$ \frac {-2}{5} + i \frac {11}{5}$
The least positive value of n if $(\frac {1+i}{1-i})^4 =1$ is
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2
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3
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4
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8
If z is a complex number, then
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|z2| >|z|2
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|z2| =|z|2
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|z2| < |z|2
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$|z^2| \geq |z|^2$
The modules of $(2-i)^6$ is
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25
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5
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125
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$\sqrt {5}$
Complex number restricted by the below equation will lie on |z-1| = |z+1|
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Parabola
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Circle
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Ellipse
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Straight line
The real value of $\theta$ for which the expression $\frac {1 + i cos \theta}{1 -2i cos \theta}$ is a real number is
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$ n \pi + \frac {\pi}{4}$
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$ n \pi \pm \frac {\pi}{2}$
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$ n \pi + (-1)^n \frac {\pi}{4}$
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None of these
Match the column
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p -> iv, q -> iii, r -> ii, c -> i
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p -> iii, q -> iv, r -> i, c -> ii
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p -> i, q -> iv, r -> ii, c -> iii
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p -> iii, q -> iv, r -> ii, c -> i
if $z^2 =i$, then z is
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$\pm ( \frac {1}{\sqrt 2} + ( \frac {i}{\sqrt 2}$
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$\pm ( \frac {1}{\sqrt 2} - ( \frac {i}{\sqrt 2}$
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$\pm ( \frac {1}{2} + ( \frac {i}{ 2}$
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$\pm ( \frac {1}{2} - ( \frac {i}{ 2}$
The value of $ 1 + i + i^2 + i^3 + i^4 + i^5 + i^6 + i^7$ is
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1
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-1
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2
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0
The principal argument of $ \frac {-16}{1 + i \sqrt 3}$ is
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$\frac { \pi}{3}$
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$\frac {2 \pi}{3}$
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$\frac { \pi}{4}$
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$\frac {- \pi}{3}$
The amplitude of $sin \frac {\pi}{5} + i (1- cos \frac {\pi}{5})$ is
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$ \frac {2 \pi}{5}$
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$ \frac { \pi}{5}$
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$ \frac { \pi}{15}$
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$ \frac { \pi}{10}$
The roots of quadratic equation $3x^2 + 7ix + 6=0$ is
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3i, 2i/3
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3i, -2i/3
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-3i, -2i/3
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-3i, 2i/3
Number of solutions of the equation $z^2 + |z|^2 = 0$ is
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0
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1
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2
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infinitely many
The roots of the equation $9x^2 -12x + 20 =0$ is
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$2 \pm 3i$
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$ \frac {2}{3} \pm \frac {4}{3} i$
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$ \frac {1}{3} \pm \frac {2}{3} i$
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$3 \pm 2i$
Match the column
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p -> iii, q -> iv, r -> i, s -> ii
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p -> iv, q -> iii, r -> i, s -> ii
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p -> iii, q -> iv, r -> ii, s -> i
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p -> i, q -> iv, r -> iii, s -> ii
if $z_1 = 1-i$ and $z_2=-1 + 2i$, then $Im(\frac {z_1z_2}{\bar{z_2}}$ is
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1/3
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2/3
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5/3
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-5/3
The equation $|z + 1 -i| − = |z -1 +i|$ represents a
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straight line
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circle
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parabola
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hyperbola
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