Recent questions tagged exercise5-2

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

asked 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

asked Apr 19, 2014 by yamini.v

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

asked Apr 19, 2014 by yamini.v

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

asked Apr 19, 2014 by yamini.v

1 answer

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

asked Apr 18, 2014 by yamini.v

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

asked 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 .

asked Apr 18, 2014 by yamini.v

1 answer

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

asked Apr 18, 2014 by yamini.v

1 answer

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

asked Apr 18, 2014 by yamini.v

1 answer

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

asked Apr 18, 2014 by yamini.v

1 answer

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

asked 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

asked Apr 18, 2014 by yamini.v

1 answer

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

asked Apr 18, 2014 by yamini.v

1 answer

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

asked Apr 18, 2014 by yamini.v

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

asked 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

asked 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 .

asked 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

asked 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 $\; \large\frac{7 \pi}{12} + \theta$

asked 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 .

asked Apr 18, 2014 by yamini.v

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

asked Apr 18, 2014 by yamini.v

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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 .

asked Apr 18, 2014 by yamini.v

1 answer

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

asked Apr 18, 2014 by yamini.v

1 answer

If a complex number lies in the third quadrant , then its conjugate lies in the ----

asked Apr 18, 2014 by yamini.v

1 answer

The conjugate of the complex number $\;\large\frac{1-i}{1+i}\;$ is

asked Apr 17, 2014 by yamini.v

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The value of $\;(-\sqrt{-1})^{4n-3}\;$ , where $\;n \in N \;$ is

asked Apr 17, 2014 by yamini.v

1 answer

The locus of $z$ satisfying $\;arg(z) = \large\frac{\pi}{3}\;$ is

asked Apr 17, 2014 by yamini.v

1 answer

If $\;|z|=2\;$ and $\;arg(z) = \large\frac{\pi}{4}\;$ , then $\;z=$

asked Apr 17, 2014 by yamini.v

1 answer

The real value of $' a '$ for which $\;3i^{3}-2ai^{2}+(1-a)i+5\;$ is real is

asked Apr 17, 2014 by yamini.v

1 answer

If $\;z_{1}\;$ and $\;z_{2}\;$ both satisfy $\;z+\overline{z} =2|z-1|\;arg(z_{1}-z_{2}) = \large\frac{\pi}{4}\;,$ then find $\;Im(z_{1}+z_{2})\;.$

asked Apr 17, 2014 by yamini.v

1 answer

Find the value of $k$ if for the complex numbers $\;z_{1}\;$ and $\;z_{2}\;,|1-\overline{z_{1}}z_{2}|^{2} - |z_{1} - z_{2}|^{2}= k (1-|z_{1}|^{2}) (1-|z_{2}|^{2})$

asked Apr 17, 2014 by yamini.v

1 answer

Find the value of a such that the sum of the squares of the roots of the equation $\;x^{2}-(a-2)x-(a+1)=0\;$ is least .

asked Apr 17, 2014 by yamini.v

1 answer

Find the value of P such that the difference of the roots of the equation $\;x^{2}-Px+8=0\;$ is $2$

asked Apr 17, 2014 by yamini.v

1 answer

Find the value of $\;2x^{4} + 5 x^{3} +7x^{2} - x+41\;,$ when $\;x=-2-\sqrt{3} i$

asked Apr 17, 2014 by yamini.v

1 answer

Locate the points for which $\; 3 < |z| < 4$

asked Apr 17, 2014 by yamini.v

1 answer

If a complex number z lies on the interior or on the boundary of a circle of radius 3 units and centre (-4,0) find the greatest and least values of $\;|z+1| \;.$

asked Apr 17, 2014 by yamini.v

1 answer

If $\;z_{1} , z_{2} ,z_{3}\;$ are complex numbers such that $\;|z_{1}|=|z_{2}|=|z_{3}|=|\large\frac{1}{z_{1}} +\large\frac{1}{z_{2}} + \large\frac{1}{z_{3}}|=1\;$ , then find the value of $\;|z_{1}+ z_{2}+z_{3}|\; .$

asked Apr 17, 2014 by yamini.v

1 answer

Let $\;z_{1}\;$ and $\;z_{2}\;$ be two complex numbers such that $\;|z_{1}+z_{2}| = |z_{1}|+|z_{2}|\;$ Then show that $\;arg(z_{1}) - arg(z_{2}) =0$

asked Apr 17, 2014 by yamini.v

1 answer

Let $\;z_{1}\;$ and $\;z_{2}\;$ be two complex numbers such that $\;\overline{z_{1} }+ i\overline{z_{2}}=0\;$ and $\;arg(z_{1} z_{2}) = \pi\;$ . Then find $\;arg(z_{1})$

asked Apr 17, 2014 by yamini.v

1 answer

If $\;|z^{2}-1| = |z|^{2}+1\;$, then show that $z$ lies on imaginary axis

asked Apr 17, 2014 by yamini.v

1 answer

If the imaginary part of $\;\large\frac{2z+1}{iz+1}\;$ is $-2$ , then show that the locus of the point representing $z$ in the argand plane is a straight line .

asked Apr 17, 2014 by yamini.v

1 answer

Solve the equation $\;z^{2} = \overline{z}\;$ where $\;z=x+iy$

asked Apr 17, 2014 by yamini.v

1 answer

If $\;(x+iy)^{\large\frac{1}{3}}= a+ib\;$ where $\;x\;,y\;,a\;,b \in R\;$ show that $\; \large\frac{x}{a} - \large\frac{y}{b} = -2 (a^{2} + b^{2})$

asked Apr 17, 2014 by yamini.v

1 answer

Evaluate : $\; (1+i)^{6} +(1-i)^{3}$

asked Apr 17, 2014 by yamini.v

1 answer

Convert the given complex number in polar form :$\;i\;$

asked Apr 10, 2014 by yamini.v

1 answer

Convert the given complex number in polar form :$\;\sqrt{3}+i\;$

asked Apr 10, 2014 by yamini.v

1 answer

Convert the given complex number in polar form :$\;-3$

asked Apr 10, 2014 by yamini.v

1 answer

Convert the given complex number in polar form :$\;-1-i\;$

asked Apr 10, 2014 by yamini.v

1 answer

Convert the given complex number in polar form :$\;-1+i\;$

asked Apr 10, 2014 by yamini.v

1 answer

Convert the given complex number in polar form :$\;1-i\;$

asked Apr 10, 2014 by yamini.v

1 answer

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