Recent questions in Complex Numbers and Quadratic Equations

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 $z=(\lambda+3)-i\sqrt{5-\lambda^2}$ ,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

Value of z satisfying the equation $\log z+\log z^2+.......+\log z^n=0$ is

asked Apr 10, 2014 by sreemathi.v

1 answer

Let $z=a(\cos\large\frac{\pi}{5}$ $+i\sin\large\frac{\pi}{5})$ $\quad a\in R,|a| < 1$ then $S=z^{2015}+z^{2016}+z^{2017}+.......$ equals

asked Apr 10, 2014 by sreemathi.v

1 answer

If $z_1$ and $z_2$ are two non zero complex numbers such that $\mid z_1+z_2\mid=\mid z_1\mid+\mid z_2\mid$ then $arg(z_1)-arg(z_2)$ is equal to

asked Apr 10, 2014 by sreemathi.v

1 answer

If $x+iy=\sqrt{\large\frac{a+ib}{c+id}}$ ,then the value of $\large\frac{(x^2+y^2)^2(c^2+d^2)}{(a^2+b^2)}$ is

asked Apr 10, 2014 by sreemathi.v

1 answer

The least value of $\mid z_1+z_2\mid$ if $z_1=24+7i$ and $|z_2|=6$ is :

asked Apr 10, 2014 by sreemathi.v

1 answer

The greatest value of $\mid z_1+z_2\mid$ if $z_1=24+7i$ and $|z_2|=6$ is :

asked Apr 10, 2014 by sreemathi.v

1 answer

If $\alpha$ and $\beta$ are distinct complex numbers with $\mid \beta\mid=1$ ,then value of $\big|\large\frac{\beta-\alpha}{1-\overline{\alpha}\beta}\big|$ equals

asked Apr 10, 2014 by sreemathi.v

1 answer

$z=\large\frac{7-i}{3-4i}$ then $z^{14}$ equals

asked Apr 10, 2014 by sreemathi.v

1 answer

No of complex numbers satisfying $\overline{z}=iz^2$ is

asked Apr 10, 2014 by sreemathi.v

1 answer

If $\alpha,\beta$ are roots of $x^2+px+q=0$ and $\omega$ is cube root of unity,then the value of $(\omega\alpha+\omega^2\beta)(\omega^2\alpha+\omega \beta)$ is

asked Apr 10, 2014 by sreemathi.v

1 answer

Given, $\omega$ is imaginary cube root of unity,the value of the expression $1(2-\omega)(2-\omega^2)+2(3-\omega)(3-\omega^2)+......(n-1)(n-\omega)(n-\omega^2)$ is

asked Apr 10, 2014 by sreemathi.v

1 answer

Equation of straight line joining complex no p and iq(where $p,q\in R$ and $p,q\neq 0)$ is :

asked Apr 10, 2014 by sreemathi.v

1 answer

The complex numbers $z_1,z_2,z_3$ are vertices of an equilateral triangle with circumcentre $z_0$ .The value of $z_1^2+z_2^2+z_3^2$ equals

asked Apr 10, 2014 by sreemathi.v

1 answer

If $\omega=\cos\large\frac{\pi}{n}$ $+i\sin\large\frac{\pi}{n}$ ,then the value of $1+\omega+\omega^2+.....+\omega^{n-1}$ is :

asked Apr 10, 2014 by sreemathi.v

1 answer

If $(x+iy)^{\large\frac{1}{3}}=a+ib$ then $\large\frac{x}{a}+\frac{y}{b}$ equals

asked Apr 10, 2014 by sreemathi.v

1 answer

If $z_k=\cos\big(\large\frac{k\pi}{10})$ $+i\sin(\large\frac{k\pi}{10})$ ,then $z_1z_2z_3z_4$ equals

asked Apr 10, 2014 by sreemathi.v

1 answer

$z=x+iy$ and $\omega=\large\frac{1-iz}{z-i}$ then $|\omega|=1$ implies that in complex plane

asked Apr 10, 2014 by sreemathi.v

1 answer

Express the given complex number in the form $\;a+ib : (-2-\large\frac{1}{3} \normalsize i)^{3}$

asked Apr 9, 2014 by yamini.v

1 answer

Express the complex number given below in the form $a+ib$ : $(5i)\;(-\large\frac{3}{5}$ $i)$

asked Apr 9, 2014 by balaji.thirumalai

1 answer

Express the given complex number in the form $\;a+ib : (\large\frac{1}{3}$ $+3i)^{3}$

asked Apr 9, 2014 by yamini.v

1 answer

Express the given complex number in the form $\;a+ib : (1-i)^{4}$

asked Apr 9, 2014 by yamini.v

1 answer

Express the given complex number in the form $\;a+ib :\;[( \normalsize \large\frac{1}{3} +\normalsize i \normalsize \large\frac{7}{3}) + (\normalsize 4 + \normalsize i \normalsize \large\frac{1}{3})-( \normalsize -\large\frac{4}{3}+ \normalsize i)]$

asked Apr 9, 2014 by yamini.v

1 answer

Express the complex number $(\large\frac{1}{5} + i\large\frac{2}{5})-(4 + i (\large\frac{5}{2}))$ in the form $a+ib$

asked Apr 9, 2014 by yamini.v

1 answer

Express the complex number $(1-i)-(-1+6i)$ in the form $a+ib$

asked Apr 9, 2014 by yamini.v

1 answer

Express the complex number $3(7+i7) + i(7 + i7)$ in the form $a+ib$

asked Apr 9, 2014 by yamini.v

1 answer

Express the complex number $i^{-39}$ in the form $a+ib$

asked Apr 9, 2014 by yamini.v

1 answer

Express the complex number $i^{9}+i^{19}$ in the form $a+bi$

asked Apr 9, 2014 by yamini.v

1 answer

For any complex number z,the minimum value of $\mid z\mid+\mid z-2i\mid$ is

asked Apr 9, 2014 by sreemathi.v

1 answer

Given, $3^{49}(x+iy)=(\large\frac{3}{2}+\frac{\sqrt 3}{2})^{100}$ $\quad y\in N$ and $x=ky$ ,then value of k is

asked Apr 9, 2014 by sreemathi.v

1 answer

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