Recent questions and answers in Complex Numbers and Quadratic Equations

if z1=4+7i, z2=1-i for what value of lamda is z1+lamdaz2, a purely real number

answered Oct 13, 2014 by pady_1

1 answer

Number of solutions of the equation $\;z^{2}+|z|^{2} =0\;$ is

answered Apr 19, 2014 by yamini.v

1 answer

The amplitude of $\; sin \large\frac{\pi}{5} + i\; \normalsize cos (1-\large\frac{\pi}{5})\;$ is

answered Apr 19, 2014 by yamini.v

1 answer

The equation $\;|z+1-i|=|z-1+i|\;$ represents a

answered Apr 19, 2014 by yamini.v

1 answer

The area of the triangle on the complex plane formed by the complex number $\;z \;,iz \;,$ and $\;z+iz\;$ is :

answered Apr 19, 2014 by yamini.v

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If the complex number $\;z=x+iy\;$ satisfies the condition $\;|z+1|=1\;$ , then z lies on

answered Apr 18, 2014 by yamini.v

1 answer

$1+i+i^{2}+i^{3} + i^{4}+i^{5}+i^{6}---+i^{2n}\;$ is

answered Apr 18, 2014 by yamini.v

1 answer

If $\;1-i\;$ is a root of the equation $\;x^{2} +ax + b=0\;$ where $\;a,b \in R\;$ , then find the values of a and b .

answered Apr 18, 2014 by yamini.v

1 answer

What is the locus of z , if amplitude of $\;z-2-3i\;$ is $\;\large\frac{\pi}{4}\;$ ?

answered Apr 18, 2014 by yamini.v

1 answer

What is the polar form of the complex number $\;(i^{25})^{3} \;$ ?

answered Apr 18, 2014 by yamini.v

1 answer

What is the principle value of amplitude of $\;1-i\;$ ?

answered Apr 18, 2014 by yamini.v

1 answer

What is the conjugate of $\; \large\frac{\sqrt{5+12 i } +\sqrt{5-12 i } } {\sqrt{5+12 i } -\sqrt{5-12 i } }$

answered Apr 18, 2014 by yamini.v

1 answer

If $\;z_{1} = \sqrt{3} + i \sqrt{3}\;$ and $\;z_{2} =\sqrt{3} + i\;$ , then find the quadrant in which $\;(\large\frac{z_{1}}{z_{2}})\;$ lies

answered Apr 18, 2014 by yamini.v

1 answer

What is the reciprocal of $\;3+ \sqrt{7} i$ ?

answered Apr 18, 2014 by yamini.v

1 answer

What is the smallest positive integer n , for which $\; (1+i)^{2n} = (1-i)^{2n}$

answered Apr 18, 2014 by yamini.v

1 answer

What is the value of $\; \large\frac{i^{4n+1} - i^{4n-1}}{2}\;$ ?

answered Apr 18, 2014 by yamini.v

1 answer

State true or false for the following : If n is a positive integer , then the value of $\;i^{n} + i^{n+1} + i^{n+2} + i^{n+3} \;$ is 0

answered Apr 18, 2014 by yamini.v

1 answer

State true or false for the following : If three complex numbers $\;z_{1} , z_{2}\;$ and $\;z_{3}\;$ are in A.P. then they lie on a circle in the complex plane .

answered Apr 18, 2014 by yamini.v

1 answer

State true or false for the following : The points representing the complex number z for which $\;|z+1| < |z-1|\;$ lies in the interior of a circle

answered Apr 18, 2014 by yamini.v

1 answer

State true or false for the following : The argument of the complex number $\;z=(1+ i\sqrt{3})(1+i)(cos \theta + i sin \theta)\;$ is $\; \large\frac{7 \pi}{12} + \theta$

answered Apr 18, 2014 by yamini.v

1 answer

State true or false for the following : If a complex number coincides with its conjugate , then the number must lie on imaginary axis .

answered Apr 18, 2014 by yamini.v

1 answer

State true or false for the following : The complex number $\;cos \theta + i sin \theta\;$ can be zero for some $\;\theta$

answered Apr 18, 2014 by yamini.v

1 answer

State true or false for the following : Multiplication of non-zero complex number by i rotates it through a right angle in the anti clock - wise direction .

answered Apr 18, 2014 by yamini.v

1 answer

If $\;(2+i)(2+2i)(2+3i)....(2+ni)=x+iy\;$ , then $\;5\;.8\;.13....(4+n^{2})=$ ----

answered Apr 18, 2014 by yamini.v

1 answer