Complex Numbers...

Mark against the correct answer in each of the following .
$$i^{273}=$$?

$$arg \left(\dfrac{2+6\sqrt{3}i}{5+\sqrt{3}i}\right)=?$$

Compare List I with List II and choose the correct answer using codes given below:

Let $$z, w$$ be complex numbers such that $$\bar z + i\bar w =0$$ and arg $$zw = \pi$$. then $$arg \ z$$ equals

The principal argument of the complex number 
$$[(1 + i)^5 (1 + \sqrt{3}i)^2] / [-2i(-\sqrt{3} +i)]$$ is

Let $$a, b $$ and $$ c $$ be real numbers such that $$ 4 a+2 b+c=0 $$ and $$ a b>0 . $$ Then the equation $$ a x^{2}+b x+c=0 $$ has

If $$ b_{1} b_{2}=2\left(c_{1}+c_{2}\right), $$ then at least one of the equations $$ x^{2}+b_{1} x $$ $$ +c_{1}=0 $$ and $$ x^{2}+b_{2} x+c_{2}=0 $$ has

The modulus and amplitude of the complex number $$\left[e^{{3}-i\dfrac{\pi}{4}}\right]^{3}$$ are respectively.

If roots of quadratic equation $$x^2-kx+4=0$$ then $$k$$ will be 

Nature of roots of quadratic equation $$4x^2-12x-9=0$$ is: