The equation of a circle is Re(z²) + 2(Im(z))² + 2Re(z) = 0, where z = x + iy. A line which passes through the center of the given circle and the vertex of the parabola, x² $$-$$ 6x $$-$$ y + 13 = 0, has y-intercept equal to ______________.

Let $$S = \left\{ {n \in N\left| {{{\left( {\matrix{ 0 & i \cr 1 & 0 \cr } } \right)}^n}\left( {\matrix{ a & b \cr c & d \cr } } \right) = \left( {\matrix{ a & b \cr c & d \cr } } \right)\forall a,b,c,d \in R} \right.} \right\}$$, where i = $$\sqrt { - 1} $$. Then the number of 2-digit numbers in the set S is _____________.

Let z₁, z₂ be the roots of the equation z² + az + 12 = 0 and z₁, z₂ form an equilateral triangle with origin. Then, the value of |a| is :

Let z and $$\omega$$ be two complex numbers such that $$\omega = z\overline z - 2z + 2,\left| {{{z + i} \over {z - 3i}}} \right| = 1$$ and Re($$\omega$$) has minimum value. Then, the minimum value of n $$\in$$ N for which $$\omega$$ⁿ is real, is equal to ______________.