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 _____________.

The value of ${\left( {{{ - 1 + i\sqrt 3 } \over {1 - i}}} \right)^{30}}$ is :

If [x] be the greatest integer less than or equal to x, then $\sum\limits_{n = 8}^{100} {\left[ {{{{{( - 1)}^n}n} \over 2}} \right]}$ is…

Let z1 and z2 be two complex numbers such that ${\overline z _1} = i{\overline z _2}$ and $\arg \left( {{{{z_1}} \over {{{\overline z…

The complex number $z=\frac{i-1}{\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}}$ is equal to :

Let f(x) be a polynomial of degree 3 such that $f(k) = - {2 \over k}$ for k = 2, 3, 4, 5. Then the value of 52 $-$ 10f(10) is equal to :