Complex Numbers...

Express the following complex numbers in the standard from $$ a+ib$$ :
$$ \dfrac{5+\sqrt{2}i}{1-\sqrt{2}i}$$

If $$a$$ and $$b$$ are the nonzero distinct roots of $$x^2 + ax + b =0$$, then the minimum vlue of $$x^2 + ax+b$$ is

The real part of $$(i - \sqrt{3})^{13}$$ is

Mark against the correct answer in each of the following .
$$i^{326}=$$?

Mark against the correct answer in each of the following .
$$i^{91}=$$?

$$(1-\sqrt{-1})(1+\sqrt{-1})(5-\sqrt{-7})(5+\sqrt{-7})=?$$

$$arg (-1+i\sqrt{3})=?$$

For any complex numbers $$z_{1}$$ and $$z_{2}$$ compare List I with with List II and choose the correct answer, using codes given below:

$$(2-3i)(-3+4i)=?$$

$$arg (1+i)=?$$