Complex Numbers...

$$z_1$$ and $$z_2$$ are two non-zero complex numbers such that $$z_1=2+4i\\z_2=5-6i$$, then $$z_2-z_1$$ equals

The imaginary part of $$t ; t \in R$$ is 

If  $$z = \cos \dfrac { \pi } { 4 } + i \sin \dfrac { \pi } { 6 } ,$$  then

Let z be a complex number such that the principal value of argument, arg $$z < 0$$. Then $$arg(-z) - arg (z)$$ is

Given $$ z _ { 1 } + 3 z _ { 2 } - 4 z _ { 3 } = 0 $$ then $$ z _ { 1 } , z _ { 2 } , z _ { 3 } $$ are

If z be a complex number satisfying $$z^{4}+z^{3}+2z^{2}+z+1=0$$ then $$\left|z\right|=$$

Express the following complex numbers in the standard form $$ a+ib$$ :
$$ \left ( \dfrac{1}{1-4i}-\dfrac{2}{1+i} \right )\left ( \dfrac{3-4i}{5+i} \right )$$

Express the following complex numbers in the standard form $$ a+ib$$ :
$$ \dfrac{\left ( 2+i \right )^{3}}{2+3i}$$

Find the modulus and argument of the following complex numbers and hence express each of them in the polar form:
$$1-i$$

Express the following complex numbers in the standard form $$ a+ib$$ :
$$ \dfrac{3-4i}{\left ( 4-2i \right )\left ( 1+i \right )}$$