Complex Numbers...

The modulus of $$\dfrac { \left( 3+2i \right) ^{ 2 } }{ \left( 4-3i \right)  } $$ is:

Number of complex numbers $$z$$ such that $$|z|=1$$ and $$\left|\dfrac {z}{z}+\dfrac {\bar {z}}{z}\right|=1$$ is

If arg $$\left( z \right) < 0,$$ then arg $$\left( { - z} \right)-arg(z)$$

Purely imaginary then find the sum of statement i $$a,b$$ 

If $$\alpha$$ and $$\beta$$ are the roots of $${ 4x }^{ 2 }-16x+c=0,$$ c>0 such that $$1<\alpha <2<\beta <3$$, then the no.of integer values of c is 

$$\sqrt { \left( \log _ { 3 } \tan x \right) }$$  is real for:

Arg $$\left\{ {\sin \frac{{8\pi }}{5} + i\left( {1 + \cos \frac{{8\pi }}{5}} \right)} \right\}$$ is equal to

Let 'z' be a complex number satisfying $$|z-2-i|\le 5,$$ Then |z-14-6i| lies in 

IF $$z_1=1+i,z_2=1-i$$ find $$z_1z_2$$

The value of the sum $$\sum _{ n=1 }^{ 13 }{ ({ i }^{ n }+{ i }^{ n+1 }) } $$ , where $$i=\sqrt { -1 } $$ , equals