The Magic Number of Kaprekar

If $z=2-i\sqrt{7}$, then $3z^3-4z^2+z+88$ is equal to

Solution set of inequality ${\text{log}}_{10}\left({\text{x}}^2-2\text{x}-2\right)\le 0$ is

A mapping $f\mathit{:}N\mathit{\to }N$, where $N$ is the set of natural numbers is defined as

$f\left(n\right)\mathit{=}\left\{\begin{array}{c}{n}^2, \text{if} n \text{is odd}\\ 2n+\mathit{1}, \text{if} n \text{is even}\end{array}\right.$

For $n\mathit{\in }N$. Then, $f$ is

If the coefficients of $r$ ^th  and $(r+1)$ ^th  terms in the expansion of ${\left(3+7x\right)}^{29}$are equal, then $r$ equals to

The value of  $\sum _{k=1}^{10}\left(\sin \frac{2k\pi }{11}+i\cos \frac{2k\pi }{11}\right)$ is