Recent questions tagged objective

If $\large\frac{1-i}{1+i}$ is a root of the equation $ax^{2}+bx+1=0$ where $a ,b $ are real then $(a , b) $is

asked May 13, 2013 by poojasapani_1

1 answer

The equation having $4-3j$ and $4+3j $ as roots is

asked May 13, 2013 by poojasapani_1

1 answer

The quadratic equation whose roots are $\pm\;i\sqrt{7} $is

asked May 13, 2013 by poojasapani_1

1 answer

If $-i+2 $ is one root of the equation $ax^{2}-bx+c=0$, then the other root is

asked May 13, 2013 by poojasapani_1

1 answer

The conjugate of $i^{13}+i^{14}+i^{15}+i^{16}$ is

asked May 12, 2013 by poojasapani_1

1 answer

The value of $i+i^{22}+i^{23}+i^{24}+i^{25}$ is

asked May 12, 2013 by poojasapani_1

1 answer

$z_{1}=4+5i,z_{2}=-3+2i$ then $\large\frac{z_{1}}{z_{2}}$is

asked May 12, 2013 by poojasapani_1

1 answer

If $ a=\cos\alpha- i \sin \alpha,b=\cos\beta-i \sin\beta,c=\cos\gamma-i\sin\gamma$ then $(a^{2} c^{2} -b^{2})/abc$ is

asked May 12, 2013 by poojasapani_1

0 answers

If $x=\cos\theta+i\sin\theta $ the value of $x^{n}+\large\frac{1}{x^{n}}$ is

asked May 12, 2013 by poojasapani_1

1 answer

If $-\overline{z}$ lies in the third quadrant then $z$ lies in the

asked May 12, 2013 by poojasapani_1

1 answer

If $z_{n}=\cos\large\frac{n\pi}{3}$$+i\sin\large\frac{n\pi}{3} $ then $z_{1}z_{2} \dots\;z_{6}$is

asked May 12, 2013 by poojasapani_1

1 answer

$\large\frac{1+e^{-i\theta}}{1+e^{i\theta}}$=

asked May 12, 2013 by poojasapani_1

1 answer

If $p$ represents the veriable complex number $z$ and if $|2z-1|=2|z|$ then the locus of $p$ is

asked May 12, 2013 by poojasapani_1

1 answer

The polar form of the complex number $(i^{25})^{3}$ is

asked May 12, 2013 by poojasapani_1

1 answer

If the point represented by the complex number $iz$ is rotated about the origin through the angle $\large\frac{\pi}{2}$ in the counter clockwise direction then the complex number representing the new position is

asked May 12, 2013 by poojasapani_1

1 answer

If the amplitude of a complex number is $\pi/2$ then the number is

asked May 12, 2013 by poojasapani_1

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If $z$ represents a complex number then arg $(z)+arg(\overline{z})$ is

asked May 12, 2013 by poojasapani_1

1 answer

The points $z_{1} , z_{2} , z_{3} , z_{4} $ in the complex plane are the vertices of a parallelogram taken in order if and only if

asked May 12, 2013 by poojasapani_1

1 answer

If $a=3+i $ and $z=2-3i$ then the points on the Argand diagram representing $az , 3az $ and $-az $ are

asked May 12, 2013 by poojasapani_1

1 answer

If $A+iB=(a_{1}+ib_{1})(a_{2}+ib_{2})(a_{3}+ib_{3}) $ then $A^{2}+B^{2}$is

asked May 11, 2013 by poojasapani_1

1 answer

The modulus of the complex number $2+i\sqrt{3}$ is

asked May 11, 2013 by poojasapani_1

1 answer

If $x^{2}+y^{2}=1$ then the value of $\large\frac{1+x+iy}{1+x-iy}$ is

asked May 11, 2013 by poojasapani_1

1 answer

If $(m-5)+i(n+4)$ is the complex conjugate of $(2m+3)+i(3n-2)$ then $(n ,m )$are

asked May 11, 2013 by poojasapani_1

1 answer

The modulus and amplitude of the complex number $[e^{3-i \pi/4}]^{3}$ is respectively

asked May 11, 2013 by poojasapani_1

1 answer

The value of $\large[\frac{-1+i\sqrt{3}}{2}]^{100}+[\frac{-1-i\sqrt{3}}{2}]^{100}$ is

asked May 11, 2013 by poojasapani_1

1 answer

The centre and the radius of the sphere given by $x^{2}+y^{2}+z^{2}-6x+8y-10z+1=0$ is

asked May 11, 2013 by poojasapani_1

1 answer

The following two lines are $ \large\frac{x-1}{2}=\frac{y-1}{-1}=\frac{z}{1}$ and $\large\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z-1}{2}$ is

asked May 11, 2013 by poojasapani_1

1 answer

The shortest distance between the parallel lines $ \large\frac{x-3}{4}=\frac{y-1}{2}=\frac{z-5}{-3} $ and $\large\frac{x-1}{4}=\frac{y-2}{2}=\frac{z-3}{3}$ is

asked May 11, 2013 by poojasapani_1

1 answer

The shortest distance between the lines $ \large\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4} $ and $\large\frac{x-2}{3}=\frac{y-4}{4}=\frac{z-5}{5}$ is

asked May 11, 2013 by poojasapani_1

1 answer

The point of intersection of the lines $\overrightarrow{r}=(-\overrightarrow{i}+\overrightarrow{2j}+\overrightarrow{3k})+\overrightarrow{t}=(-\overrightarrow{2i}+\overrightarrow{j}+\overrightarrow{k}) $ and $\overrightarrow{r}=(\overrightarrow{2i}+\overrightarrow{3j}+\overrightarrow{5k})+\overrightarrow{s}=(\overrightarrow{i}+\overrightarrow{2j}+\overrightarrow{3k}) $ is

asked May 11, 2013 by poojasapani_1

1 answer

The point of intersection of the lines $\large\frac{x-6}{-6}=\frac{y+4}{4}=\frac{z-4}{-8} $ and $\large\frac{x+1}{2}=\frac{y+2}{4}=\frac{z+3}{-2}$ is

asked May 11, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}=\overrightarrow{i}-\overrightarrow{2j}+\overrightarrow{3k}$ and $\overrightarrow{b}=\overrightarrow{3i}+\overrightarrow{j}+\overrightarrow{2k}$ then a unit vector perpendicular to $\overrightarrow{a}$ and $\overrightarrow{b}$ is

asked May 11, 2013 by poojasapani_1

1 answer