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

If $\big|z-\large\frac{4}{z}\big|$$=2$,the maximum value of $\mid z\mid$ is equal to

asked Apr 9, 2014 by sreemathi.v

1 answer

If $z_1+z_2+z_3=0$ and $\mid z_1\mid=\mid z_2\mid=\mid z_3\mid=1$ then value of $z_1^2+z_2^2+z_3^2$ equals

asked Apr 9, 2014 by sreemathi.v

1 answer

Let $z,\omega$ be two comlex numbers such that $\overline{z}+i\overline{\omega}=0$ and $arg(z\omega)=\pi$, then $arg(z)$ equal to

asked Apr 9, 2014 by sreemathi.v

1 answer

If $\mid z+4\mid\leq 3$,then maximum value of $\mid z+1\mid$ is

asked Apr 9, 2014 by sreemathi.v

1 answer

If $\mid z^2-1\mid=\mid z\mid^2+1$ then $z$ lies on

asked Apr 9, 2014 by sreemathi.v

1 answer

If $\mid z\mid=1$ and $z\neq \pm 1$ then $\large\frac{z}{1-z^2}$ lie on

asked Apr 9, 2014 by sreemathi.v

1 answer

Let $z=\begin{vmatrix}1&2+3i&4+5i\\2-3i&6&7+8i\\4-5i&7-8i&-9\end{vmatrix}$,then

asked Apr 9, 2014 by sreemathi.v

1 answer

If $\omega$ is a complex root of unity, one root of the equation $\begin{vmatrix}x+1 &\omega&\omega^2\\\omega&x+\omega^2&1\\\omega^2&1&x+\omega\end{vmatrix}=0$ is

asked Apr 9, 2014 by sreemathi.v

1 answer

$z=\large\frac{1}{1-\cos \theta+i\sin \theta}$.Re(z) is equal to

asked Apr 9, 2014 by sreemathi.v

1 answer

Given $x=2+5i$, the value of $x^3-5x^2+33x-19$ is

asked Apr 9, 2014 by sreemathi.v

1 answer

If $\omega=\large\frac{z-\perp}{z+1}$$\quad (z\neq -\perp)$ and $\mid z\mid =\perp$ then $Re(\omega)$ equals

asked Apr 9, 2014 by sreemathi.v

1 answer

$z$ and $\omega$ are two non zero complex numbers such that $\mid z\mid=\mid \omega\mid$ and $arg(z)+arg(\omega)=\pi$.Then $z$ equals

asked Apr 9, 2014 by sreemathi.v

1 answer

If $z\neq 0$ is a complex no having arg=$\large\frac{\pi}{4}$,then

asked Apr 9, 2014 by sreemathi.v

1 answer

Let $a,b$ be real numbers between $0\; and\; 1$ such that $z_1=1+bi,z_2=a+i$ and $z_3=0$ forms an equilateral triangle then

asked Apr 9, 2014 by sreemathi.v

1 answer

The complex numbers $\sin x+i\cos 2x$ and $\cos x-i\sin 2x$ are conjugate for

asked Apr 9, 2014 by sreemathi.v

1 answer

If complex numbers $z_1,z_2,z_3$ represents vertices of an equilateral triangle and $\mid z_1\mid=\mid z_2\mid=\mid z_3\mid$ then

asked Apr 9, 2014 by sreemathi.v

1 answer

If $z$ is a complex number such that $\left|\; z \;\right| \geq 2$ then the minimum value of $\large\left|\normalsize z \normalsize + \large\frac{1}{2} \right |$

asked Apr 6, 2014 by balaji.thirumalai

0 answers

If the coefficients of $x^3$ and $x^5$ in the expansion of $(1+ax+bx^2)(1-2x)^{18}$ in powers of $x$ are both zero, then $(a,b)$ is equal to:

asked Apr 6, 2014 by balaji.thirumalai

0 answers

If $\large\frac{1}{a},\frac{1}{b},\frac{1}{c} $ are in A.P., then the equation $a(b-c)x^2+b(c-a)x+c(a-b)=0$ has

asked Aug 8, 2013 by rvidyagovindarajan_1

1 answer

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

The cube roots of $-1$ are?

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

If $z_1,z_2$ are any two complex numbers and $a,b$ are two real numbers, then $|az_1-bz_2|^2+|bz_1+az_2|^2=?$

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

If $z$ is a complex number and $a$ is real, then $(z+a)(\overline z+a)=?$

asked Jul 28, 2013 by rvidyagovindarajan_1

1 answer

The complex numbers $z$ satisfying $|z|-4=0$ and $ |z-i|-|z+5i|=0$ are ?

asked Jul 27, 2013 by rvidyagovindarajan_1

1 answer

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