Recent questions tagged ch5

If the ratio of the roots of $ax^2+bx+c=0$ is equal to the roots of the equation $ x^2+x+1=0$, then $a,b,c$ are in ?

asked Aug 8, 2013 by rvidyagovindarajan_1

1 answer

If $\alpha$ is the fifth root of unity, then the value of $log_2 |1+\alpha+\alpha^2+\alpha^3-\large\frac{1}{\alpha}$$|=?$

asked Aug 6, 2013 by rvidyagovindarajan_1

1 answer

If for any complex number $z$, $|z-1|=1$, then $\large\frac{z-2}{z}=?$

asked Aug 6, 2013 by rvidyagovindarajan_1

1 answer

If $|z+\overline z|+|z-\overline z|=8$ then $z$ lies on ?

asked Aug 6, 2013 by rvidyagovindarajan_1

1 answer

If $z_r(r=1,2,......7)$ are the roots of $(z_r+1)^7+z_r^7=0$, then $\sum\limits_{r=1}^{7} Re(z_r)=?$

asked Aug 6, 2013 by rvidyagovindarajan_1

1 answer

If $p,q\in \{1,2,3,4\},$ then the number of equations of the form $px^2+qx+1=0$ having real roots is?

asked Aug 6, 2013 by rvidyagovindarajan_1

1 answer

If $3+\sqrt 2 i$ is a root of of $x^2+px+q=0$, then $(p,q)=?$

asked Aug 6, 2013 by rvidyagovindarajan_1

1 answer

If $z$ is a complex number having non zero imaginary part and $z^2+z+1=a$ where $a$ is real, then $a$ cannot take which of the following values?

asked Aug 5, 2013 by rvidyagovindarajan_1

1 answer

The value of $b$ for which the eqns., $x^2+bx-1=0,\:x^2+x+b=0$ have one common root is

asked Aug 5, 2013 by rvidyagovindarajan_1

1 answer

If the eqns., $x^2-6x+a=0$ and $x^2-5x+6=0$ have one root in common and the other roots are in the ratio 4:3, then the common root is

asked Aug 5, 2013 by rvidyagovindarajan_1

1 answer

If $\cos\theta+2\cos\alpha+3\cos\beta=\sin\theta+2\sin\alpha+3\sin\beta=0$, then $\sin\;3\theta+8\sin\;3\alpha+27\sin\;3\beta=?$

asked Aug 2, 2013 by rvidyagovindarajan_1

1 answer

If $(\cos\alpha+i\sin\alpha)(\cos2\alpha+i\sin2\alpha)....(\cos n\alpha+i \sin n\alpha)$ = 1, then $\alpha$ = ?

asked Aug 2, 2013 by rvidyagovindarajan_1

1 answer

The common roots to the equations $z^3+2z^2+2z+1=0\:\:and\:\:z^{149}+z^{100}+1=0$ are

asked Aug 2, 2013 by rvidyagovindarajan_1

1 answer

For any complex number $z$, the minimum value of $|z|+|z-1|=?$

asked Aug 1, 2013 by rvidyagovindarajan_1

1 answer

If $z_r=cos(\large\frac{\pi}{3^r})$$+isin(\large\frac{\pi}{3^r})$, where $r=1,2,3...........then \:\:z_1.z_2.z_3.....................\infty=?$

asked Aug 1, 2013 by rvidyagovindarajan_1

1 answer

If $a=\cos\alpha+i \sin\alpha$, $b=\cos\beta+i \sin\beta$, $c=\cos\gamma+i\sin\gamma$ and $\large\frac{b}{c}+\frac{c}{a}+\frac{a}{b}$ = 1, then $\cos(\beta-\gamma)+\cos(\gamma-\alpha)+\cos(\alpha-\beta)$ = ?

asked Aug 1, 2013 by rvidyagovindarajan_1

1 answer

If $R_e\bigg(\large\frac{z-8i}{z+6}\bigg)$$=0$, then $z$ lies in the curve

asked Aug 1, 2013 by rvidyagovindarajan_1

1 answer

If $n$ is a positive integer, then $(1+i)^n+(1-i)^n=?$

asked Jul 31, 2013 by rvidyagovindarajan_1

1 answer

$\large\frac{(cosx+isinx)(cosy+isiny)}{(cotu+i)(1+itanv)}=?$

asked Jul 31, 2013 by rvidyagovindarajan_1

1 answer

If $ \large\frac{3}{2+\cos\theta+i\sin\theta}=$$x+iy$, then $ (x-1)(x-3)=?$

asked Jul 31, 2013 by rvidyagovindarajan_1

1 answer

If $\omega$ is cube root of $1$ and $\alpha,\beta,\gamma$ are cube roots of $p$ , then for any real numbers $x,y,z$the value of $\large\frac{x\alpha+y\beta+z\gamma}{x\beta+y\gamma+z\alpha}$ is ?

asked Jul 28, 2013 by rvidyagovindarajan_1

1 answer

For any integer $ n$, the argument of $z=\large\frac{(\sqrt 3+i)^{4n+1}}{(1-\sqrt 3 i)^{4n}}$ is ?

asked Jul 28, 2013 by rvidyagovindarajan_1

1 answer

The value of $\sum\limits_{n=1}^{13} (i^n+i^{n+1})=?$

asked Jul 28, 2013 by rvidyagovindarajan_1

1 answer

If $z_1,z_2,z_3,z_4$ are the roots of $z^4=1$, then $\sum\limits_{i=1}^4 z_i^3$=?

asked Jul 28, 2013 by rvidyagovindarajan_1

1 answer

If conjugate of $(x+iy)(1-2i)=1+i$, then $(x,y)=?$

asked Jul 28, 2013 by rvidyagovindarajan_1

1 answer

The complex number $\large\frac{1+2i}{1-i}$ lies in which quadrant?

asked Jul 28, 2013 by rvidyagovindarajan_1

1 answer

The argument of $\large\frac{1-\sqrt 3i}{1+\sqrt 3i}=?$

asked Jul 28, 2013 by rvidyagovindarajan_1

1 answer