Recent questions tagged ch5

Let $\;z_{1}=2-i\;,z_{2}=-2+i\;$. Find (i)$\;Re(\large\frac{z_{1}z_{2}}{\overline{z_{1}}})\;,$ (ii) $\;Im(\large\frac{1}{z_{1} \overline{z_{2}}})$

asked Apr 14, 2014 by yamini.v

1 answer

If $\;a+ib =\large\frac{(x+i)^{2}}{2x^{2}+1}\;$ , find $\;a^{2} +b^{2}$

asked Apr 11, 2014 by yamini.v

1 answer

If $\;z_{1}=2-i\;,z_{2}=1+i\;$ find $\;|\large\frac{z_{1}+z_{2}+1}{z_{1}-z_{2}+i}|$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;21x^{2}-28x+10=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;27x^{2}-10x+1=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;x^{2}-2x+\large\frac{3}{2}=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;3x^{2}-4x+\large\frac{20}{3}=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Convert the following in the polar form : $\;\large\frac{1+3i}{1-2i}$

asked Apr 11, 2014 by yamini.v

1 answer

Convert the following in the polar form : $\;\large\frac{1+7i}{(2-i)^{2}}$

asked Apr 11, 2014 by yamini.v

1 answer

If $\;x-iy=\sqrt{\large\frac{a-ib}{c-id}}\;$ what is the value of $\;(x^{2}+y^{2})^{2}$?

asked Apr 11, 2014 by yamini.v

1 answer

Reduce $\;(\large\frac{1}{1-4i}- \large\frac{2}{1+i})\;(\large\frac{3 -4i}{5+i})\;$ to the standard form

asked Apr 11, 2014 by yamini.v

1 answer

For any two complex numbers $\;z_{1}\;$ and $\;z_{2}\;$, what is the value of $\; Re(z_{1} z_{2}) $?

asked Apr 11, 2014 by yamini.v

1 answer

Evaluate : $\;[i^{18} +(\large\frac{1}{i})^{25}]^{3}$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;x^{2}+\large\frac{x}{\sqrt{2}}+1=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;x^{2}+x+\large\frac{1}{\sqrt{2}}=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;\sqrt{3}x^{2}-\sqrt{2}x+3\sqrt{3}=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;\sqrt{2}x^{2}+x+\sqrt{2}=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;x^{2}-x+2=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;x^{2}+3x+5=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;-x^{2}+x-2=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;x^{2}+3x+9=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;2x^{2}+x+1=0\;$

asked Apr 10, 2014 by yamini.v

1 answer

Solve the equation : $\;x^{2}+3=0\;$

asked Apr 10, 2014 by yamini.v

1 answer

Convert the given complex number in polar form :$\;i\;$

asked Apr 10, 2014 by yamini.v

1 answer

Convert the given complex number in polar form :$\;\sqrt{3}+i\;$

asked Apr 10, 2014 by yamini.v

1 answer

Convert the given complex number in polar form :$\;-3$

asked Apr 10, 2014 by yamini.v

1 answer

Convert the given complex number in polar form :$\;-1-i\;$

asked Apr 10, 2014 by yamini.v

1 answer

Convert the given complex number in polar form :$\;-1+i\;$

asked Apr 10, 2014 by yamini.v

1 answer

Convert the given complex number in polar form :$\;1-i\;$

asked Apr 10, 2014 by yamini.v

1 answer

The greatest +ve argument of complex number satisfying $|z-4|=Re(z)$ is :

asked Apr 10, 2014 by sreemathi.v

1 answer

Find the modulus and the argument of the complex number $\;z=-\normalsize \sqrt{3} + \normalsize i$

asked Apr 10, 2014 by yamini.v

1 answer

Given $z=1-t+i\sqrt{t^2+t+2}$ wher $t$ is a real parameter.The locus of z in Argand plane is

asked Apr 10, 2014 by sreemathi.v

1 answer

Given $z^2+z|z|+|z^2|=0$ the locus of z is

asked Apr 10, 2014 by sreemathi.v

1 answer

Find the modulus and the argument of the complex number $\;z=-\normalsize 1- \normalsize i\sqrt{3}$

asked Apr 10, 2014 by yamini.v

1 answer

If p and q are distinct prime numbers then the no of distinct imaginary numbers which are $p^{th}$ as well as $q^{th}$ root of unity are

asked Apr 10, 2014 by sreemathi.v

1 answer

Which point in Argand plane is equidistant from roots of equation $(z+1)^4=16z^4$?

asked Apr 10, 2014 by sreemathi.v

1 answer

Express the following expression in the form $\;\normalsize a + \normalsize ib : \large\frac{(\normalsize 3 + \normalsize i \sqrt{5})(\normalsize 3 - \normalsize i \sqrt{5})}{(\normalsize \sqrt{3} + \normalsize i \sqrt{2})-(\normalsize \sqrt{3} - \normalsize i \sqrt{2})}$

asked Apr 10, 2014 by yamini.v

1 answer

If $z$ satisfies $|z+1| < |z+2|$ then $\omega=3z+2+i$,satisfies

asked Apr 10, 2014 by sreemathi.v

1 answer

Find the multiplicative inverse of the complex number $\;\normalsize -i\;$

asked Apr 10, 2014 by yamini.v

1 answer

The maximum distance from origin to the point z satisfying the equation $\big|z+\large\frac{1}{z}\big|=a$ is

asked Apr 10, 2014 by sreemathi.v

1 answer

Find the multiplicative inverse of the complex number $\;\sqrt{5} +3 \normalsize i\;$

asked Apr 10, 2014 by yamini.v

1 answer

Given $arg\bigg(z_1-\large\frac{\Large\frac{z}{|z|}}{\Large\frac{z}{|z|}}\bigg)=\frac{\pi}{2}$ and $\big|\large\frac{z}{|z|}-$$z_1\big|=3$,then $|z_1|$ equals

asked Apr 10, 2014 by sreemathi.v

1 answer

If $ y = 500e^{\large 7x} + 600e^{\large -7x}$, what is $\large\frac{d^2y}{dx^2}$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

If $ y = 3 \cos \: (\log x ) + 4 \sin ( \log x )$, show that $x^2y_2 + xy_1 $

asked Apr 10, 2014 by balaji.thirumalai

1 answer

If $ y = 5 \cos x - 3 \sin x $ , what is $\large\frac{d^2y}{dx^2} $

asked Apr 10, 2014 by balaji.thirumalai

1 answer

If $z=(\lambda+3)-i\sqrt{5-\lambda^2}$,then locus of $z$ is

asked Apr 10, 2014 by sreemathi.v

1 answer

Complex no lying on angle bisector of $z_1$ and $z_2$ where $z_1=3+\sqrt 3i$ and $z_2=2\sqrt 3+6i$ is

asked Apr 10, 2014 by sreemathi.v

1 answer

If $z$ is a complex number having least absolute value and $|z-2+2i|=1$ then $z=$

asked Apr 10, 2014 by sreemathi.v

1 answer

Find the multiplicative inverse of the complex number $\;\normalsize 4-\normalsize 3 \normalsize i\;$

asked Apr 10, 2014 by yamini.v

1 answer

If $\alpha$ is $n^{th}$ root of unity,the value of $1+2\alpha+3\alpha^2+...$ upto n terms is equal to

asked Apr 10, 2014 by sreemathi.v

1 answer

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