Let $$z_k=\cos \left(\frac{2 k \pi}{10}\right)+i \sin \left(\frac{2 k \pi}{10}\right) ; k=1,2, \ldots \ldots \ldots$$ 9, then $$\frac{1}{10}\left\{\left|1-z_1\right|\left|1-z_2\right| \ldots .\left|1-z_a\right|\right\}$$ equals to

The condition in order that $$Z_1, Z_2, Z_3$$ are vertices of an isosceles triangle right angled at $$z_2$$, is

If $$(1+i)(2 i+1)(1+3 i) \ldots(1+n i)=x+i y$$, then $$2 \cdot 5 \cdot 10 \ldots\left(1+n^2\right)$$ is equal to

The non-zero solutions of the equation $$z^2+|z|=0$$, where $$z$$ is a complex number, are