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Questions asked by geethradh
Questions
42
questions
0
answers selected
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 $\frac{a^{2}b^{2}+c^{2}}{abc}\; = \; 2\; cos \; 2\left ( \alpha \;+\;\beta \;+\;\gamma \right )$
tnstate
class12
bookproblem
ch3
sec3
exercise3-4
q10
q10-2
p158
asked
Apr 19, 2013
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 $\sqrt{abc}\; + \; \frac{1}{\sqrt{abc}}\; = \; 2\; cos\left ( \alpha \;+\;\beta \;+\;\gamma \right )$
tnstate
class12
bookproblem
ch3
sec3
exercise3-4
q10
q10-1
p158
asked
Apr 19, 2013
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}}$$= \;2\cos \;\left ( m\alpha + n\beta \right )$
tnstate
class12
bookproblem
ch3
sec3
exercise3-4
q9
p158
mar-2007
modelpaper
asked
Apr 19, 2013
1
answer
If $x+\large\frac{1}{x}$$ =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 )$
tnstate
class12
bookproblem
ch3
sec3
exercise3-4
q8
q8-2
p158
asked
Apr 19, 2013
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}} $$= 2 \cos \left ( m\theta -n\phi \right )$
tnstate
class12
bookproblem
ch3
sec3
exercise3-4
q8
q8-1
p158
asked
Apr 19, 2013
1
answer
If $x +\large\frac{1}{x} = $$2\; cos\;\theta $ prove that $x^{n} -\large \frac{1}{x^{n}}= $$2i\; sin\;n\theta $
tnstate
class12
bookproblem
ch3
sec3
exercise3-4
q7
q7-2
p158
asked
Apr 18, 2013
1
answer
If $\; x+\large\frac{1}{x}= $$\;2\;\cos\;\theta \; $ prove that $\;x^{n}+\large\frac{1}{x^{n}}$$= \;2\;\cos\;n\theta\; $
tnstate
class12
bookproblem
ch3
sec3
exercise3-4
q7
q7-1
p158
asked
Apr 18, 2013
1
answer
If $ \alpha$ and $\beta $ are the roots of $x^{2}-2x+4=0$. Prove that $\alpha ^{n}-\beta ^{n}=i2^{n+1}sin\large\frac{n\pi }{3}$ and calculate $\alpha ^{9}-\beta ^{9}$, where n $\in$ N?
tnstate
class12
bookproblem
ch3
sec3
exercise3-4
q6
p158
oct-2006
oct-2008
mar-2009
modelpaper
asked
Apr 18, 2013
1
answer
If $\alpha $ and $\beta$ are the roots of the equation $ x^{2}-2px+\left ( p^{2} + q^{2}\right )=0 $ and $ tan \; \theta =\large \frac{q}{y+p} $ show that $ \large\frac{\left (y+\alpha \right )^{n}-\left ( y+\beta \right )^{n}}{\alpha -\beta }$ = $ q^{n-1}\large\frac{sin \;n\theta }{sin\;^{n}\theta }$
tnstate
bookproblem
class12
ch3
exercise3-4
sec3
q5
p158
mar-2007
oct-2009
modelpaper
asked
Apr 18, 2013
1
answer
Prove that $\left ( 1+\mathit{i} \right )^{4n}$ and $\left ( 1+\mathit{i} \right )^{4n+2}$ are real and purely imaginary respectively.
tnstate
class12
bookproblem
ch3
exercise3-4
q4
q4-4
p157
asked
Apr 16, 2013
1
answer
Prove that $\left ( 1+ \cos \; \theta + \mathit{i}\sin \; \theta \right )^{\mathit{n}} + \left ( 1+ \cos \; \theta - \mathit{i}sin \; \theta \right )^{\mathit{n}} = 2^{\mathit{n+1}} \cos ^{\mathit{n}}\left ( \large\frac{\theta}{2} \right )$$ \cos \;\large\frac{n\theta }{2}$
tnstate
class12
bookproblem
ch3
exercise3-4
q4
q4-3
p157
asked
Apr 16, 2013
1
answer
Prove that $\left ( 1+ \mathit{i\sqrt{3}} \right )^{\mathit{n}} + \left ( 1- \mathit{i\sqrt{3}} \right )^{\mathit{n}} = 2^{n+1} \cos \; \large\frac{n\pi}{3}$
tnstate
class12
bookproblem
ch3
exercise3-4
q4
q4-2
p157
jun-2008
asked
Apr 16, 2013
1
answer
Prove that $\left ( 1+\mathit{i} \right )^{\mathit{n}} + \left ( 1-\mathit{i} \right )^{\mathit{n}} = 2^{\large\frac{n+2}{2}} \cos \; \large\frac{n\pi}{4}$
tnstate
class12
bookproblem
ch3
exercise3-4
q4
q4-1
p157
oct-2007
may-2008
may-2010
modelpaper
asked
Apr 16, 2013
1
answer
If $ \cos\;\alpha + \cos\;\beta + \cos\;\gamma = 0 = \sin \;\alpha + \sin \;\beta + \sin \;\gamma $, prove that $\cos^{2}\;\alpha + \cos^{2}\;\beta + \cos^{2}\;\gamma = \sin^{2} \alpha + \sin^{2}\beta + \sin^{2}\gamma = \large\frac{3}{2}$.
tnstate
bookproblem
class12
ch3
exercise3-4
q3
q3-5
p157
asked
Apr 10, 2013
1
answer
If $ \cos\;\alpha + \cos\;\beta + \cos\;\gamma = 0 = \sin \;\alpha + \sin \;\beta + \sin \;\gamma $, prove that $\sin 2\alpha + \sin 2\beta + \sin 2\gamma = 0$
tnstate
class12
bookproblem
ch3
exercise3-4
q3
q3-4
p157
jun-2006
modelpaper
asked
Apr 8, 2013
1
answer
If $ cos\;\alpha + cos\;\beta + cos\;\gamma = 0 = sin\;\alpha + sin\;\beta + sin\;\gamma $, prove that $ cos\;2\alpha + cos 2\;\beta + cos\;2\gamma = 0$
tnstate
class12
bookproblem
exercise3-4
q3
q3-3
p157
asked
Apr 5, 2013
0
answers
If $ cos \;\alpha + cos \;\beta + cos \;\gamma = 0 = sin \;\alpha + sin \;\beta + sin \; \gamma $, prove that $ sin \;3\alpha \; + \;sin \;3\beta + sin \;3\gamma = 3 sin\left ( \alpha\; + \;\beta\; + \;\gamma \;\right )\Large$
tnstate
bookproblem
class12
exercise3-4
q3
q3-2
p157
asked
Apr 5, 2013
0
answers
If $\cos \alpha + cos \beta + cos \gamma = 0 = sin \alpha + sin \beta + sin \gamma$, prove that $cos 3\alpha + cos 3\beta + cos 3\gamma = 3 cos\left ( \alpha +\beta + \gamma \right )$
tnstate
class12
bookproblem
ch3
sec3
exercise3-4
q3
q3-1
p157
asked
Apr 4, 2013
1
answer
Simplify: $\Large\frac{\left (cos \;\alpha + \mathit{i} sin \; \alpha \right )^{3}}{\left (sin \;\beta + \mathit{i} cos \;\beta \right)^{4} } \Large$
tnstate
class12
bookproblem
ch3
sec3
exercise3-4
q2
p157
asked
Apr 4, 2013
1
answer
Simplify: $\Large\frac{\left ( cos2 \theta -\mathit{i}sin2 \theta \right )^{7} \left ( cos 3 \theta +\mathit{i} sin3 \theta \right )^{-5}}{\left (cos 4 \theta + \mathit{i} sin4 \theta \right )^{12} \left ( cos 5 \theta -\mathit{i}sin5 \theta \right )^{-6}}\Large$
tnstate
class12
bookproblem
ch3
sec3
exercise3-4
q1
p157
asked
Apr 4, 2013
1
answer
Solve : $6x^{4}-25x^{3}+32x^{2}+3x-10=0$ given that one of the roots is $2-i$.
tnstate
class12
ch3
sec3
exercise3-3
q3
p152
asked
Apr 3, 2013
1
answer
Solve the equation $x^{4}-4x^{3}+11x^{2}-14x+10=0$ if one root is $1+2i$.
tnstate
bookproblem
ch3
sec3
exercise3-3
q2
p152
jun-2009
modelpaper
asked
Apr 3, 2013
1
answer
Solve the equation $x^{4}-8x^{3}+24x^{2}-32x+20$ = 0 if $3+\mathit{i}$ is a root.
tnstate
class12
bookproblem
ch3
sec3
exercise3-3
q1
p152
mar-2009
modelpaper
asked
Apr 3, 2013
1
answer
If arg $\left ( z-1 \right )$ = $\large\frac{\pi}{6}$ and arg $\left ( z+1 \right )$ = 2$\large\frac{\pi}{3}$ then prove that $\left | z \right |=1$
tnstate
class12
bookproblem
ch3
sec3
exercise3-2
q7
p150
asked
Apr 2, 2013
1
answer
Express the following complex numbers in polar form. $1 - \mathit{i}$
tnstate
class12
bookproblem
sec3
ch3
exercise3-2
q6
q6-4
p150
asked
Apr 2, 2013
1
answer
Express the following complex numbers in polar form. $-1 - \mathit{i}$
tnstate
class12
bookproblem
sec3
ch3
exercise3-2
q6
q6-3
p150
asked
Apr 2, 2013
1
answer
Express the following complex number in polar form. $-1 + \mathit{i}\sqrt{3}$
tnstate
class12
bookproblem
ch3
sec3
exercise3-2
q6
q6-2
p150
asked
Apr 2, 2013
1
answer
Express the following complex number in polar form. $2 + 2\sqrt{3}\mathit{i}$
tnstate
class12
bookproblem
sec3
ch3
exercise3-2
q6
q6-1
p150
asked
Apr 2, 2013
1
answer
Prove that the points representing the complex numbers $\left ( 7+5\mathit{i} \right )$, $\left ( 5+2\mathit{i} \right )$, $\left ( 4+7\mathit{i} \right )$ and $\left ( 2+4\mathit{i} \right )$ form a parallelogram. (Plot the points and use midpoint formula).
tnstate
class12
bookproblem
ch3
sec3
exercise3-2
q5
p150
asked
Apr 2, 2013
1
answer
If $\left ( 1+\mathit{i} \right )\left ( 1+2\mathit{i} \right )\left ( 1+3\mathit{i} \right )... \left ( 1+\mathit{ni} \right )=\mathit{x+iy}$, show that 2.5.10 ... $\left ( 1+n^{2} \right )$ = $ x^{2}+y^{2}$
tnstate
class12
bookproblem
ch3
sec3
exercise3-2
q1
p150
asked
Apr 2, 2013
1
answer
For what values of $\mathit{x}$ and $\mathit{y}$, the numbers $-3+\mathit{ix^{2}y}$ and $\mathit{x^{2}}+y+4\mathit{i}$ are complex conjugate of each other$?$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
q5
p131
asked
Apr 1, 2013
1
answer
Find the real values of $\mathit{x}$ and $\mathit{y}$ for which the following equation: $\sqrt{x^{2}+3x+8} + \left ( x+4 \right )\mathit{i} = \mathit{y}\left (2 + \mathit{i} \right )$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
q4
q4-3
p130
asked
Apr 1, 2013
1
answer
Find the real values of $\mathit{x}$ and $\mathit{y}$ for which the following equation: $\large\frac{\left ( 1+\mathit{i} \right )\mathit{x}-2\mathit{i}}{3+\mathit{i}} + \frac{\left ( 2-3\mathit{i} \right )\mathit{y}+\mathit{i}}{3-\mathit{i}} = $$\mathit{i}$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
q4
q4-2
p130
asked
Apr 1, 2013
1
answer
Find the real values of $\mathit{x}$ and $\mathit{y}$ for which the following equation: $\left ( 1-\mathit{i} \right )\mathit{x} + \left ( 1+\mathit{i} \right )\mathit{y} = 1-3\mathit{i}$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
q4
q4-1
p130
asked
Apr 1, 2013
1
answer
Find the least positive integer $\mathit{n}$ such that $\left ( \large\frac{1+\mathit{i}}{1-\mathit{i}} \right )^{\mathit{n}}$$ = 1$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
q3
p130
asked
Apr 1, 2013
1
answer
Find the real and imaginary parts of the following complex numbers: $\left ( 2+i \right )\left ( 3-2i \right )$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
q2
q2-3
p130
asked
Apr 1, 2013
1
answer
Find the real and imaginary parts of the following complex numbers: $\large\frac{2+5i}{4-3i}$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
p130
q2
q2-2
asked
Apr 1, 2013
1
answer
Find the real and imaginary parts of the following complex numbers: $\large\frac{1}{1+i}$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
p130
q2
q2-1
asked
Apr 1, 2013
1
answer
Express the following in the standard form $a + ib$: $\large\frac{i^{4}+i^{9}+i^{16}}{3-2i^{8}-i^{10}-i^{15}}$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
p130
q1
q1-4
asked
Apr 1, 2013
1
answer
Express the following in the standard form $a + ib$: $\left ( -3+i \right )\left ( 4-2i \right )$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
p130
q1
q1-3
asked
Apr 1, 2013
1
answer
Express the following in the standard form $a+ib$: $\large\frac{\left ( 1+i \right )\left ( 1-2i \right )}{1+3i}$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
p130
q1
q1-2
asked
Apr 1, 2013
1
answer
Express the following in the standard form $a + ib$: $\large\frac{2\left ( i-3 \right )}{\left ( 1+i \right )^{2}}$
tnstate
class12
bookproblem
ch3
sec3
q1
q1-1
p130
exercise3-1
asked
Apr 1, 2013
1
answer
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