If $z = \sum_{n=0}^{2026} i^n$, where $i = \sqrt{-1}$, then one of the values of $\sqrt{z}$ is...

Point A$(5, 12)$ rotated about the origin O in the XY-plane through an angle of $30^\circ$ in the anticlockwise direction to a new position B. The ordinate of point B is...

The smallest positive integer $n$ for which $\dfrac{(1 + i)^n}{(1 - i)^{n-2}}$ is a real number, is ...

The area of the triangle whose vertices are $i, \omega$ and $\omega^2$ is (Where $\omega$ is a complex cube root of unity other than $1, i$ is an imaginary number)__________ sq.units