Complex Numbers...

Modulus of $$\dfrac{\cos \theta - i\sin \theta}{\sin \theta - i \cos \theta}$$ is

If $$\cfrac{\pi}{3}$$ and $$\cfrac{\pi}{4}$$ are the arguments of $${z}_{1}$$ and $${\overline { z }  }_{ 2 }$$, then the value of arg $$({z}_{1}{z}_{2})$$ is

$$n\in N,\ { \left( \dfrac { 1+i }{ \sqrt { 2 }  }  \right)  }^{ 8n }+{ \left( \dfrac { 1-i }{ \sqrt { 2 }  }  \right)  }^{ 8n }=$$

The complex number $$z$$ satisfies $$z+|z|=2+8i$$. The value of $$|z|$$ is

For a complex number $$z$$, the minimum value of $$\left| z \right| + \left| {z - 1} \right|$$ is

The value of $$\sum\limits_{n = 1}^{13} {\left( {{i^n} + {i^{n + 1}}} \right)} $$, where $$i = \sqrt { - 1} $$ equals:

If $$\left| {{z_1}} \right| =  = 1,\left| {{z_2}} \right| = 2,$$, then the value of $${\left| {{z_1} + {z_2}} \right|^2} + {\left| {{z_1} - {z_2}} \right|^2}$$ is equal to 

The modulus of the complex quantity $$(2-3i)(-1+7i)$$.

If A and B be two complex numbers satisfying $$\dfrac{A}{B}+\dfrac{B}{A}=1$$. Then the two points represented by A and B and the origin form the vertices of

$$3+2\ i\ \sin \theta$$ will be real, if $$\theta=$$