I1.1 If $|x+\sqrt{5}|+|y-\sqrt{5}|+|z|=0$, determine $\alpha=x^{2}+y^{2}+z^{2}$.
I1.2 If $\beta$ is the sum of all digits of the product $\underbrace{11111 \cdots 11}_{\alpha 1_{1}^{\prime} s} \times \underbrace{99999 \ldots 99}_{\alpha 9 \text { s's }}$, determine the value of $\beta$.
I1.3 Suppose that the real function $f(x)$ satisfies $f(x y)=f(x) f(y)$ for all real numbers $x$ and $y$, and $f(1)<1$. Determine the value of $\gamma=f(\beta)+100-\beta$.

I1.4 If $n$ is a positive integer and $f(n)=2^{n}+2^{n-1}+2^{n-2}+\ldots+2^{2}+2^{1}+1$, determine the value of $\delta=f(\gamma)$.