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Recent questions tagged exercise5-misc

Convert the complex number $\;z=\large\frac{i-1}{cos \large\frac{\pi}{3} + i sin \large\frac{\pi}{3}}\;$ in the polar form

asked Apr 16, 2014 by yamini.v

1 answer

Find real $\;\theta\;$ such that $\;\large\frac{3 +2i sin \theta}{1-2isin\theta}\;$ is purely real .

asked Apr 16, 2014 by yamini.v

1 answer

If $\;x+iy = \large\frac{a+ib}{a-ib}\;$, prove that $\;x^{2} + y^{2} =1$

asked Apr 16, 2014 by yamini.v

1 answer

Find the modulus and argument of the complex number $\; \large\frac{1}{1+i}$

asked Apr 16, 2014 by yamini.v

1 answer

Find the modulus and argument of the complex number $\; \large\frac{1+i}{1-i}$

asked Apr 16, 2014 by yamini.v

1 answer

Find the conjugate of $\;\large\frac{(3-2i)(2+3i)}{(1+2i)(2-i)}$

asked Apr 16, 2014 by yamini.v

1 answer

If $\;(\large\frac{1+i}{1-i})^{m}=1\;$ then find the least positive integral value of m

asked Apr 15, 2014 by yamini.v

1 answer

Find the number of non - zero integral solutions of the equation $\;|1-i|^{x}=2^{x}$

asked Apr 15, 2014 by yamini.v

1 answer

If $\;\alpha\;$ and $\;\beta\;$ are different complex numbers with $\;|\beta=1|\;$ , then find $\;|\large\frac{\beta-\alpha}{1-\overline{\alpha} \beta}|$

asked Apr 15, 2014 by yamini.v

1 answer

If $\;(x+iy)^{3}=u+iv\;$ , then show that $\; \large\frac{u}{x} + \large\frac{v}{y} = 4(x^{2}-y^{2})$

asked Apr 15, 2014 by yamini.v

1 answer

Find the modulus of $\;\large\frac{1+i}{1-i} - \large\frac{1-i}{1+i}$

asked Apr 15, 2014 by yamini.v

1 answer

Find the real numbers x and y if $\;(x-iy)(3+5i)\;$ is the conjugate of $\;-6-24i$

asked Apr 14, 2014 by yamini.v

1 answer

Find the modulus and argument of the complex number $\;\large\frac{1+2i}{1-3i}$

asked Apr 14, 2014 by yamini.v

1 answer

Let $\;z_{1}=2-i\;,z_{2}=-2+i\;$. Find (i)$\;Re(\large\frac{z_{1}z_{2}}{\overline{z_{1}}})\;,$ (ii) $\;Im(\large\frac{1}{z_{1} \overline{z_{2}}})$

asked Apr 14, 2014 by yamini.v

1 answer

If $\;a+ib =\large\frac{(x+i)^{2}}{2x^{2}+1}\;$ , find $\;a^{2} +b^{2}$

asked Apr 11, 2014 by yamini.v

1 answer

If $\;z_{1}=2-i\;,z_{2}=1+i\;$ find $\;|\large\frac{z_{1}+z_{2}+1}{z_{1}-z_{2}+i}|$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;21x^{2}-28x+10=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;27x^{2}-10x+1=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;x^{2}-2x+\large\frac{3}{2}=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;3x^{2}-4x+\large\frac{20}{3}=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Convert the following in the polar form : $\;\large\frac{1+3i}{1-2i}$

asked Apr 11, 2014 by yamini.v

1 answer

Convert the following in the polar form : $\;\large\frac{1+7i}{(2-i)^{2}}$

asked Apr 11, 2014 by yamini.v

1 answer

If $\;x-iy=\sqrt{\large\frac{a-ib}{c-id}}\;$ what is the value of $\;(x^{2}+y^{2})^{2}$?

asked Apr 11, 2014 by yamini.v

1 answer

Reduce $\;(\large\frac{1}{1-4i}- \large\frac{2}{1+i})\;(\large\frac{3 -4i}{5+i})\;$ to the standard form

asked Apr 11, 2014 by yamini.v

1 answer

For any two complex numbers $\;z_{1}\;$ and $\;z_{2}\;$, what is the value of $\; Re(z_{1} z_{2}) $?

asked Apr 11, 2014 by yamini.v

1 answer

Evaluate : $\;[i^{18} +(\large\frac{1}{i})^{25}]^{3}$

asked Apr 11, 2014 by yamini.v

1 answer

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