If the equation, x² + bx + 45 = 0 (b $$ \in $$ R) has conjugate complex roots and they satisfy |z +1| = 2$$\sqrt {10} $$ , then :

If $${{3 + i\sin \theta } \over {4 - i\cos \theta }}$$, $$\theta $$ $$ \in $$ [0, 2$$\theta $$], is a real number, then an argument of
sin$$\theta $$ + icos$$\theta $$ is :

If $${\mathop{\rm Re}\nolimits} \left( {{{z - 1} \over {2z + i}}} \right) = 1$$, where z = x + iy, then the point (x, y) lies on a :

Let z $$ \in $$ C with Im(z) = 10 and it satisfies $${{2z - n} \over {2z + n}}$$ = 2i - 1 for some natural number n. Then :