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Recent questions tagged ch5
Questions
State true or false for the following : Multiplication of non-zero complex number by i rotates it through a right angle in the anti clock - wise direction .
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 18, 2014
by
yamini.v
1
answer
If $\;(2+i)(2+2i)(2+3i)....(2+ni)=x+iy\;$ , then$\;5\;.8\;.13....(4+n^{2})=$----
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 18, 2014
by
yamini.v
1
answer
If a complex number lies in the third quadrant , then its conjugate lies in the ----
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 18, 2014
by
yamini.v
1
answer
The conjugate of the complex number $\;\large\frac{1-i}{1+i}\;$ is
sat
math
trigonometry
cbse
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
The value of $\;(-\sqrt{-1})^{4n-3}\;$ , where $\;n \in N \;$ is
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
The locus of $z$ satisfying $\;arg(z) = \large\frac{\pi}{3}\;$ is
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
If $\;|z|=2\;$ and $\;arg(z) = \large\frac{\pi}{4}\;$ , then $\;z=$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
The real value of $' a '$ for which $\;3i^{3}-2ai^{2}+(1-a)i+5\;$ is real is
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
If $\;z_{1}\;$ and $\;z_{2}\;$ both satisfy $\;z+\overline{z} =2|z-1|\;arg(z_{1}-z_{2}) = \large\frac{\pi}{4}\;,$ then find $\;Im(z_{1}+z_{2})\;.$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
Find the value of $k$ if for the complex numbers $\;z_{1}\;$ and $\;z_{2}\;,|1-\overline{z_{1}}z_{2}|^{2} - |z_{1} - z_{2}|^{2}= k (1-|z_{1}|^{2}) (1-|z_{2}|^{2})$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
Find the value of a such that the sum of the squares of the roots of the equation $\;x^{2}-(a-2)x-(a+1)=0\;$ is least .
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
Find the value of P such that the difference of the roots of the equation $\;x^{2}-Px+8=0\;$ is $2$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
Find the value of $\;2x^{4} + 5 x^{3} +7x^{2} - x+41\;,$ when $\;x=-2-\sqrt{3} i$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
Locate the points for which $\; 3 < |z| < 4$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
If a complex number z lies on the interior or on the boundary of a circle of radius 3 units and centre (-4,0) find the greatest and least values of $\;|z+1| \;.$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
If $\;z_{1} , z_{2} ,z_{3}\;$ are complex numbers such that $\;|z_{1}|=|z_{2}|=|z_{3}|=|\large\frac{1}{z_{1}} +\large\frac{1}{z_{2}} + \large\frac{1}{z_{3}}|=1\;$ , then find the value of $\;|z_{1}+ z_{2}+z_{3}|\; .$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
Let $\;z_{1}\;$ and $\;z_{2}\;$ be two complex numbers such that $\;|z_{1}+z_{2}| = |z_{1}|+|z_{2}|\;$ Then show that $\;arg(z_{1}) - arg(z_{2}) =0$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
Let $\;z_{1}\;$ and $\;z_{2}\;$ be two complex numbers such that $\;\overline{z_{1} }+ i\overline{z_{2}}=0\;$ and $\;arg(z_{1} z_{2}) = \pi\;$ . Then find $\;arg(z_{1})$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
If $\;|z^{2}-1| = |z|^{2}+1\;$, then show that $z$ lies on imaginary axis
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
If the imaginary part of $\;\large\frac{2z+1}{iz+1}\;$ is $-2$ , then show that the locus of the point representing $z$ in the argand plane is a straight line .
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
Solve the equation $\;z^{2} = \overline{z}\;$ where $\;z=x+iy$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
If $\;(x+iy)^{\large\frac{1}{3}}= a+ib\;$ where $\;x\;,y\;,a\;,b \in R\;$ show that $\; \large\frac{x}{a} - \large\frac{y}{b} = -2 (a^{2} + b^{2})$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
Evaluate : $\; (1+i)^{6} +(1-i)^{3}$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-2
exemplar
asked
Apr 17, 2014
by
yamini.v
1
answer
Convert the complex number $\;z=\large\frac{i-1}{cos \large\frac{\pi}{3} + i sin \large\frac{\pi}{3}}\;$ in the polar form
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-misc
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
Find real $\;\theta\;$ such that $\;\large\frac{3 +2i sin \theta}{1-2isin\theta}\;$ is purely real .
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-misc
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
If $\;x+iy = \large\frac{a+ib}{a-ib}\;$, prove that $\;x^{2} + y^{2} =1$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-misc
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
Find the modulus and argument of the complex number $\; \large\frac{1}{1+i}$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-misc
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
Find the modulus and argument of the complex number $\; \large\frac{1+i}{1-i}$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-misc
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
Find the conjugate of $\;\large\frac{(3-2i)(2+3i)}{(1+2i)(2-i)}$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-misc
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
Solve $\; \sqrt{5} x^{2} + x + \sqrt{5}=0 $
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-6
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
Solve $\;x^{2} + x + 1=0 $
sat
math
trigonometry
cbse
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-6
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
Solve $\;x^{2}+2 =0 \;$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-6
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
Convert the complex number $\;\large\frac{-16}{1+i \sqrt{3}} \;$ into polar form
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-5
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
Represents the complex number $\;z=1+ \sqrt{3} i \;$ in the polar form
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-5
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
Express the following in the form $\;a+ib : i^{-35}$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-4
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
Express the following in the form $\;a+ib : \large\frac{5 + \sqrt{2} i }{1 - \sqrt{2} i}$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exercise5-4
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
Find the multiplicative inverse of $\;2 - 3 i$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
Express $\;(- \sqrt{3} + \sqrt{-2})(2 \sqrt{3} - i)\;$ in the form $\;a+ib$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
Express $\;(5-3i)^{3}\;$ in the form of $\;a+ib$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
Express the following in the form of $\;a+bi : (-i) \; (2i)\;(-\large\frac{1}{8}i)^{3}$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
Express the following in the form of $\;a+bi : (-5i) \; (\large\frac{1}{8}i)$
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
If $\;4x+i(3x-y)=3+i (-6)\;$ where x and y are real numbers , then find the values of x and y
cbse
math
class11
ch5
complex-numbers-and-quadratic-equations
exemplar
asked
Apr 16, 2014
by
yamini.v
1
answer
If the equation $ax^2+bx+c=0$ $(a > 0)$ has roots $\alpha$ and $\beta$ such that $ \alpha < -2$ and $\beta > 2$ then,
jeemain
math
class11
complex-numbers-and-quadratic-equations
ch5
difficult
asked
Apr 16, 2014
by
sreemathi.v
1
answer
Sum of rational roots of $x^5=\large\frac{133x-78}{133-78x}$ is
jeemain
math
class11
complex-numbers-and-quadratic-equations
ch5
difficult
asked
Apr 16, 2014
by
sreemathi.v
1
answer
Sum of all integral roots of $(\log_5x)^2+\log_{5x}(\large\frac{5}{x})$$=1$ is
jeemain
math
class11
complex-numbers-and-quadratic-equations
ch5
difficult
asked
Apr 16, 2014
by
sreemathi.v
1
answer
Given $x+y+z=4$ and $x^2+y^2+z^2=6$.The range of z is $[\large\frac{2}{3}$$,k]$.The value of k is
jeemain
math
class11
complex-numbers-and-quadratic-equations
ch5
difficult
asked
Apr 16, 2014
by
sreemathi.v
1
answer
Given,for three distinct real numbers a,b,c $\in R,a(a^2+p)=b(b^2+p)=c(c^2+p)$.The value of $a+b+c$ is
jeemain
math
class11
complex-numbers-and-quadratic-equations
ch5
difficult
asked
Apr 16, 2014
by
sreemathi.v
1
answer
The least integral value of m for which every solution of inequality $1 \leq x\leq 2$ is solution of the inequality $x^2-mx+1 < 0$
jeemain
math
class11
complex-numbers-and-quadratic-equations
ch5
difficult
asked
Apr 16, 2014
by
sreemathi.v
1
answer
Number of polynomials p(x) with integral coefficients satisfying the condition p(1)=2 and p(3)=1 are
jeemain
math
class11
complex-numbers-and-quadratic-equations
ch5
difficult
asked
Apr 16, 2014
by
sreemathi.v
1
answer
The real value of a for which the roots $x_1,x_2,x_3$ of $x^3-6x^2+ax-a=0$ satisfy $(x_1-3)^3+(x_2-3)^3+(x_3-3)^3=0$ is
jeemain
math
class11
complex-numbers-and-quadratic-equations
ch5
difficult
asked
Apr 16, 2014
by
sreemathi.v
1
answer
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