Recent questions tagged ch5

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