Recent questions tagged complex-numbers-and-quadratic-equations

The solution of the equation $xlog2+log(1+2^x)-log6=0$

asked Jul 27, 2013 by rvidyagovindarajan_1

1 answer

The solution set of the equation $|x^2+x|=x^2+x$ is

asked Jul 27, 2013 by rvidyagovindarajan_1

1 answer

If the equations $x^2+bx+c=0$ and $x^2+cx+b=0$ have one common root, then

asked Jul 27, 2013 by rvidyagovindarajan_1

1 answer

If one root of the eqn., $x^2+px+12=0$ is 4, while the eqn., $x^2+px+q=0$ has equal roots, then the value of $q$=?

asked Jul 27, 2013 by rvidyagovindarajan_1

1 answer

If $p>0,\:q>0$, then the roots of $x^2-px-q=0$ are

asked Jul 27, 2013 by rvidyagovindarajan_1

1 answer

The quadratic eqn., whose one root is $2-\sqrt 3i$ is given by ?

asked Jul 27, 2013 by rvidyagovindarajan_1

1 answer

If the roots of the eqn., $ax^2+bx+c=0$ are reciprocal to each other then,

asked Jul 27, 2013 by rvidyagovindarajan_1

1 answer

If the eqn., $x^2-m(2x-8)-15=0$ has equal roots, then $m=?$

asked Jul 27, 2013 by rvidyagovindarajan_1

1 answer

The numerical difference of the roots of $x^2-6x+6=0$ is ?

asked Jul 27, 2013 by rvidyagovindarajan_1

1 answer

If $a>0$, then $\sqrt {a+\sqrt {a+\sqrt{a+............}}}$=?

asked Jul 27, 2013 by rvidyagovindarajan_1

1 answer

The ratio of roots of $x^2+bx+c=0$ is same as the ratio of the roots of $x^2+qx+r=0$. Then which of the following is true?

asked Jul 26, 2013 by rvidyagovindarajan_1

1 answer

The number of roots of the eqn., $x-\large\frac{2}{x-1}$$=1-\large\frac{2}{x-1}$ is

asked Jul 25, 2013 by rvidyagovindarajan_1

1 answer

The product of all the roots of the eqn., $x^2-|x|-6=0$ is ?

asked Jul 25, 2013 by rvidyagovindarajan_1

1 answer

If the complex numbers $z_1,\:z_2,\:z_3$ represent the vertices $A,\:B,\:C$ of a parallelogram, then the fourth vertex $D$ is ?

asked Jul 25, 2013 by rvidyagovindarajan_1

1 answer

If $(1+i)(1+2i)(1+3i).....(1+ni)=x+iy$, then $2.5.10.....(1+n^2)$ = ?

asked Jul 25, 2013 by rvidyagovindarajan_1

1 answer

If $\alpha,\:\beta$ are roots of the equation $x^2+x+1=0$ then the equation whose roots are $\alpha^{19}\:\:and\:\:\beta^7$ is ?

asked Jul 24, 2013 by rvidyagovindarajan_1

1 answer

The number of solutions to the equation $|x|^2+3|x|+2=0$ is

asked Jul 24, 2013 by rvidyagovindarajan_1

1 answer

If $ix^2-x+12i=0$ then $x$ = ?

asked Jul 24, 2013 by rvidyagovindarajan_1

1 answer

The value of $\large\frac{1}{i}-\frac{1}{i^2}+\frac{1}{i^3}-\frac{1}{i^4}$ = ?

asked Jul 24, 2013 by rvidyagovindarajan_1

1 answer

The value of $\large\frac{1-i}{1+i}$ = ?

asked Jul 24, 2013 by rvidyagovindarajan_1

1 answer

If $y=\sqrt {x^2+6x+8}$, then the value of $\sqrt {1+iy}+\sqrt {1-iy}$= ?

asked Jul 24, 2013 by rvidyagovindarajan_1

1 answer

If $z=2-3i$ then the value of $z^2-4z+14$ = ?

asked Jul 24, 2013 by rvidyagovindarajan_1

1 answer

If $-3+ix^2y$ and $x^2+y+4i$ are conjugate of each other then $(x,y)$= ?

asked Jul 23, 2013 by rvidyagovindarajan_1

1 answer

If $z_1,z_2$ are complex numbers such that $\large\frac{2z_1}{3z_2}$ is purely imaginary the the value of $\bigg|\large\frac{z_1-z_2}{z_1+z_2}\bigg|$ is ?

asked Jul 23, 2013 by rvidyagovindarajan_1

1 answer

If $z_1,z_2$ are two complex numbers such that $\large|\frac{z_1+z_2}{z_1-z_2}|=1,$ then $\large\frac{z_1}{z_2}$ is ?

asked Jul 23, 2013 by rvidyagovindarajan_1

1 answer

If $z\:\:and\:\:w$ are two non zero complex numbers such that $|zw|=1$ and $Arg(z)-Arg(w)=\large\frac{\pi}{2},$ then $\overline z w$ = ?

asked Jul 23, 2013 by rvidyagovindarajan_1

1 answer

If $2-i$ is a root of the eqn., $ax^2+12x+b$, where $a$ and $b$ are real then the value of $ab$ = ?

asked Jul 22, 2013 by rvidyagovindarajan_1

1 answer

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

asked Jul 22, 2013 by rvidyagovindarajan_1

1 answer

If $z,\omega$ are complex numbers such that $\overline z+i\omega=0$, then the $arg \:z=?$

asked Jul 21, 2013 by rvidyagovindarajan_1

1 answer

If the equation $(a+1)x^2-(a+2)x+(a+3)=0$ has roots of equal magnitude and opposite signs, then the roots are

asked Jul 21, 2013 by rvidyagovindarajan_1

1 answer

$|z+\overline z|=|z-\overline z|$ represents ?

asked Jul 21, 2013 by rvidyagovindarajan_1

1 answer

One of the values of $(i)^{\large\frac{1}{3}}$ is

asked Jul 21, 2013 by rvidyagovindarajan_1

1 answer

The value of $\sqrt i+\sqrt{-i}$ = ?

asked Jul 21, 2013 by rvidyagovindarajan_1

1 answer

If $|z_1|=|z_2|=|z_3|=$ $\large|\frac{1}{z_1}+\frac{1}{z_2}+\frac{1}{z_3}|$$=1$, then $|z_1+z_2+z_3|$ = ?

asked Jul 20, 2013 by rvidyagovindarajan_1

1 answer

If $\alpha,\beta $ are real and $z$ is complex number and $z^2+\alpha z +\beta=0$ has two distinct roots on the line $R_e z=1,$ then the values of $\beta$=?

asked Jul 18, 2013 by rvidyagovindarajan_1

1 answer

The roots of $ax^2+bx+c=0$ are $r$ and $s$. For the roots of $x^2+px+q=0$ to be $r^2$ and $s^2$, what must be the value of $p$ ?

asked Jul 17, 2013 by rvidyagovindarajan_1

1 answer

The sum of all real roots of the equation: $|x-2|^2+|x-2|-2=0$ is ?

asked Jul 17, 2013 by rvidyagovindarajan_1

1 answer

If $z$ is a complex number so that $iz^2-\overline z=0$, then $|z|= ?$

asked Jul 16, 2013 by rvidyagovindarajan_1

1 answer

If $\large\frac{c+i}{c-i}$$=a+ib$, then $a^2+b^2$ = ?

asked Jul 16, 2013 by rvidyagovindarajan_1

1 answer

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

asked Jul 16, 2013 by rvidyagovindarajan_1

1 answer

If $z$ is any complex number then $\large\frac{\overline z}{|z|^2}$$= ?$

asked Jul 16, 2013 by rvidyagovindarajan_1

1 answer

The equation $z^2=\overline z$ has how many solutions ?

asked Jul 16, 2013 by rvidyagovindarajan_1

1 answer

The integral solution of the equation $(1-i)^x=2^x$ is?

asked Jul 15, 2013 by rvidyagovindarajan_1

1 answer

The complex number $z$ satisfying the equation $arg\large(\frac{z-1}{z+1})=\frac{\pi}{4}$ represents ?

asked Jul 15, 2013 by rvidyagovindarajan_1

1 answer

If $arg(z)<0$, then $arg(-z)-arg(z)$ = ?

asked Jul 15, 2013 by rvidyagovindarajan_1

1 answer

If the complex numbers $sinx+icos2x$ and $cosx-isin2x$ are conjugate to each other, then $x=?$

asked Jul 15, 2013 by rvidyagovindarajan_1

1 answer

$z+\overline z=0$ if and only if

asked Jul 15, 2013 by rvidyagovindarajan_1

1 answer

If the ratio of the roots of $ax^2+bx+c=0$ is equal to the ratio of the roots of $px^2+qx+r=0$ and if $D_1,\:D_2$ are their discriminants respectively, then $D_1:D_2=?$

asked Jul 14, 2013 by rvidyagovindarajan_1

1 answer

If the roots of the equation $x^2-4x-log_3 a=0$ are real, then the least value of $a$ is ?

asked Jul 14, 2013 by rvidyagovindarajan_1

1 answer

If the roots of the equation $x^3+bx^2+cx-1=0$ form an increasing G.P., then $b$ lies in which interval?

asked Jul 13, 2013 by rvidyagovindarajan_1

1 answer

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