Recent questions tagged sec3

$P$ represents the variable complex number $z$.Find the locus of $P$,if $Re\bigg(\large\frac{z-1}{z+i}\bigg)$$=1$

asked Jun 10, 2013 by sreemathi.v

1 answer

$P$ represents the variable complex number $z$.Find the locus of $P$,if $\mid z-5i\mid=\mid z+5i\mid$

asked Jun 10, 2013 by sreemathi.v

1 answer

$P$ represents the variable complex number $z$.Find the locus of $P$,if $Im\bigg[\large\frac{2z+1}{iz+1}\bigg]$$=-2$

asked Jun 10, 2013 by sreemathi.v

1 answer

Prove that the triangle formed by the points representing the complex numbers $(10+8i),(-2+4i)$ and $(-11+31i)$ on the Argand plane is right angled.

asked Jun 10, 2013 by sreemathi.v

1 answer

If $z^2=(0,1)$ find $z$.

asked Jun 7, 2013 by sreemathi.v

1 answer

Find the square root of $(-8-6i)$

asked Jun 7, 2013 by sreemathi.v

1 answer

In the following cases,find the distance of each of the given points from the corresponding given plane $(c)\;$Point (2,3,-5);Plane $(x+2y-2z-9=0)$

asked Jun 4, 2013 by sreemathi.v

1 answer

In the following cases,find the distance of each of the given points from the corresponding given plane $(b)\;$Point (3,-2,1);Plane $(2x-y+2z+3=0)$

asked Jun 4, 2013 by sreemathi.v

1 answer

In the following cases,find the distance of each of the given points from the corresponding given plane (d)Point(-6,0,0),Plane $2x-3y+6z-2=0$

asked May 23, 2013 by rvidyagovindarajan_1

1 answer

Find the $\perp$ distance of the point (2,3,-5) from the plane $x+2y-2z-9=0$

asked May 22, 2013 by rvidyagovindarajan_1

1 answer

Find the $\perp$ distance of the point (3,-2,1) from the plane $2x-y+2z+3=0$

asked May 22, 2013 by rvidyagovindarajan_1

1 answer

Determine whether the given planes are parallel or perpendicular, and in case they are neither, then find the angles between them.$(e)\; 4x + 8y + z -8 = 0 $ and $ y + z -4 =0$

asked May 22, 2013 by rvidyagovindarajan_1

1 answer

Determine whether the given planes are parallel or perpendicular, and in case they are neither ,then find the angles between them. $(d)\; 2x -y + 3z -1 = 0 \: and\: 2x -y + 3z + 3 = 0 $

asked May 22, 2013 by rvidyagovindarajan_1

1 answer

Determine whether the given planes are parallel or perpendicular, and in case they are neither, then find the angles between them. $(c)\; 2x -2y + 4z + 5 = 0$ and $3x -3y + 6z - 1 = 0 $

asked May 22, 2013 by rvidyagovindarajan_1

1 answer

Determine whether the given planes are parallel or perpendicular, and in case they are neither, then find the angle between them. $(b)\; 2x + y + 3z - 2 = 0 \: and\: x -2y + 5 = 0 $

asked May 22, 2013 by rvidyagovindarajan_1

1 answer

Find the equations of the planes that passes through three points, $(b)\; (1, 1, 0), (1, 2, 1), (-2, 2, -1) $

asked May 13, 2013 by rvidyagovindarajan_1

1 answer

Find the vector and cartesian equations of the planes $(b) \quad \text{that passes through the point} \; (1, 4, 6) \; \text{and the normal to the plane is } \hat i-2\hat j + \hat k $

asked May 10, 2013 by rvidyagovindarajan_1

1 answer

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane $(d)\;5y + 8 = 0 $

asked May 9, 2013 by rvidyagovindarajan_1

1 answer

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane $(c)\; x + y + z = 1 $

asked May 9, 2013 by rvidyagovindarajan_1

1 answer

Find the Cartesian equation of the following planes: (c) $ r .[(s - 2t)\hat i + (3- t) \hat j +(2 s + t) \hat k] = 15$

asked May 8, 2013 by rvidyagovindarajan_1

1 answer

Find the Cartesian equation of the plane $(b)\; \overrightarrow r . (2\hat i +3\hat j - 4\hat k) = 1 $

asked May 8, 2013 by rvidyagovindarajan_1

1 answer

In each of the following cases determine the direction cosines of the normal to the plane and the distance from origin(d) $5y+8=0$

asked May 6, 2013 by rvidyagovindarajan_1

1 answer

In each of the following cases determine the direction cosines of the normal to the plane and the distance from origin(c) $2x+3y-z=5$

asked May 6, 2013 by rvidyagovindarajan_1

1 answer

In each of the following cases,determine the direction cosines of the normal to the plane and also the distance from origin(b) $x+y+z=1$

asked May 6, 2013 by rvidyagovindarajan_1

1 answer

If $a \; =\; cos \; 2\alpha \; + \; i \; sin \; 2\alpha , \; b \; =\; cos\; 2\beta + i\; sin\; 2\beta\; $ and $\;c\; = \; cos \; 2\gamma\; + \; i sin\; 2\gamma$ prove that $\frac{a^{2}b^{2}+c^{2}}{abc}\; = \; 2\; cos \; 2\left ( \alpha \;+\;\beta \;+\;\gamma \right )$

asked Apr 19, 2013 by geethradh

0 answers

If $a \; =\; cos \; 2\alpha \; + \; i \; sin \; 2\alpha , \; b \; =\; cos\; 2\beta + i\; sin\; 2\beta\; $ and $\;c\; = \; cos \; 2\gamma\; + \; i sin\; 2\gamma$ prove that $\sqrt{abc}\; + \; \frac{1}{\sqrt{abc}}\; = \; 2\; cos\left ( \alpha \;+\;\beta \;+\;\gamma \right )$

asked Apr 19, 2013 by geethradh

0 answers

If $x\;=\cos\;\alpha +i\sin\;\alpha\;;\; y\;= \cos\;\beta + i\sin \;\beta $ prove that $x^{m}y^{n} \;+\large \frac{1}{x^{m}y^{n}}$$= \;2\cos \;\left ( m\alpha + n\beta \right )$

asked Apr 19, 2013 by geethradh

1 answer

If $x+\large\frac{1}{x}$$ =2\cos\;\theta $ and $y+\large\frac{1}{y}$$=2 \cos \;\phi$ show that $\large\frac{x^{m}}{y^{n}} - \frac{y^{n}}{x^{m}}$$ = 2i \;sin\left ( m\theta -n\phi \right )$

asked Apr 19, 2013 by geethradh

1 answer

If $x+\large\frac{1}{x}$$ =2\cos\;\theta $ and $y+\large\frac{1}{y}=$$2 \cos \;\phi$ show that $\large\frac{x^{m}}{y^{n}}+ \frac{y^{n}}{x^{m}} $$= 2 \cos \left ( m\theta -n\phi \right )$

asked Apr 19, 2013 by geethradh

1 answer

If $x +\large\frac{1}{x} = $$2\; cos\;\theta $ prove that $x^{n} -\large \frac{1}{x^{n}}= $$2i\; sin\;n\theta $

asked Apr 18, 2013 by geethradh

1 answer

If $\; x+\large\frac{1}{x}= $$\;2\;\cos\;\theta \; $ prove that $\;x^{n}+\large\frac{1}{x^{n}}$$= \;2\;\cos\;n\theta\; $

asked Apr 18, 2013 by geethradh

1 answer

If $ \alpha$ and $\beta $ are the roots of $x^{2}-2x+4=0$. Prove that $\alpha ^{n}-\beta ^{n}=i2^{n+1}sin\large\frac{n\pi }{3}$ and calculate $\alpha ^{9}-\beta ^{9}$, where n $\in$ N?

asked Apr 18, 2013 by geethradh

1 answer

If $\alpha $ and $\beta$ are the roots of the equation $ x^{2}-2px+\left ( p^{2} + q^{2}\right )=0 $ and $ tan \; \theta =\large \frac{q}{y+p} $ show that $ \large\frac{\left (y+\alpha \right )^{n}-\left ( y+\beta \right )^{n}}{\alpha -\beta }$ = $ q^{n-1}\large\frac{sin \;n\theta }{sin\;^{n}\theta }$

asked Apr 18, 2013 by geethradh

1 answer

If $\cos \alpha + cos \beta + cos \gamma = 0 = sin \alpha + sin \beta + sin \gamma$, prove that $cos 3\alpha + cos 3\beta + cos 3\gamma = 3 cos\left ( \alpha +\beta + \gamma \right )$

asked Apr 4, 2013 by geethradh

1 answer

Simplify: $\Large\frac{\left (cos \;\alpha + \mathit{i} sin \; \alpha \right )^{3}}{\left (sin \;\beta + \mathit{i} cos \;\beta \right)^{4} } \Large$

asked Apr 4, 2013 by geethradh

1 answer

Simplify: $\Large\frac{\left ( cos2 \theta -\mathit{i}sin2 \theta \right )^{7} \left ( cos 3 \theta +\mathit{i} sin3 \theta \right )^{-5}}{\left (cos 4 \theta + \mathit{i} sin4 \theta \right )^{12} \left ( cos 5 \theta -\mathit{i}sin5 \theta \right )^{-6}}\Large$

asked Apr 4, 2013 by geethradh

1 answer

Solve : $6x^{4}-25x^{3}+32x^{2}+3x-10=0$ given that one of the roots is $2-i$.

asked Apr 3, 2013 by geethradh

1 answer

Solve the equation $x^{4}-4x^{3}+11x^{2}-14x+10=0$ if one root is $1+2i$.

asked Apr 3, 2013 by geethradh

1 answer