Complex Numbers...

Argument and modules of $$[\dfrac{1+i}{1-i}]^{2\pi i}$$ are respectively................. 

If $$z_{1}$$ and $$z_{2}$$ are two non zero complex numbers such that $$|z_{1}+z_{2}|=|z_{1}|+|z_{2}|$$ then $$arg\ z_{1} $$-$$arg\ z_{2}$$ is equal to

If $$\theta$$ and $$\phi$$ are the roots of the equation $$8x^{2}+22x+5=0$$, then

The figure formed by four points $$1+0i;-1+0i,3+4i$$ and $$\cfrac{25}{-3-4i}$$ on the argand plane is

The amplitude of $$\cfrac { 1+\sqrt { 3i }  }{ \sqrt { 3 } +1 } $$ is

If $$z=(3+7i)(p+iq)$$, where $$p,q\in I-\left\{ 0 \right\} $$, is a purely imaginary, then minimum value of $${ \left| z \right|  }^{ 2 }$$ is

If $$z=\dfrac{\sqrt{3}}{2}+\dfrac{1}{2}i$$ then $$z\bar{z}$$ is

If $$Z = \frac{{1 - \sqrt 3 i}}{{1 + \sqrt 3 i}}$$ then find $$arg(z).$$

If $$\left| {z + 2 - i} \right| = 5$$ then the maximum value of $$\left| {3z + 9 - 7i} \right|$$ is 

What is the modulus of following complex number:$$-2+2\sqrt { 3i } $$