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> Let $z\in\mathbb{C}$ such that $\left|z-a\right|=\sqrt{a^2-b^2}$, $a>b>0$. Calculate $\left|\frac{b-z}{b+z}\right|$.
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I tried to amplify with the conjugate and try to work something out… or square the first relation but couldn't get anywhere…

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> Let $a\in\mathbb{C}$. Calculate the value of the expression
>  $$E=\left|a+\frac12\right|^2+i\left|a+i\frac12\right|^2-(1+i)\left|a\right|^2-\frac14(1+i).$$
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Here give your answer in function of $a$.