Complex Numbers...

The modulus of the complex number $$z$$ such that $$\left| z + 3 - i\right | = 1$$ and $$\arg{z} = \pi$$ is equal to

The roots of the equation $$(3b+c-4a)x^2+(3c+a-4b)x+(3a+b-4c)= 0$$ are 

$$\frac { { z }_{ 2 }-{ 2z }_{ 2 } }{ { z }_{ 2 }-{ z }_{ 1 }{ z }_{ 2 } } $$ is unimodular then

If $$Z=\sin \frac {6\pi}5+i(1+\cos \frac {6\pi }5)$$ then

This equation $$(x-5)^{11}+(x-5^{2})^{11}+....+(x-5^{11})^{11}=0$$ has 

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

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

Argument and modulus of $$\left[ \frac { 1 + i } { 1 - i } \right] ^ { 2013 }$$ are respectively $$\ldots \ldots \ldots$$

If the roots of the equation $${ x }^{ 2 }-8x+({ a }^{ 2 }-6a)=0$$ are real, then

Find the modules and amplitude for each of the following complex numbers