The modulus of $\mathrm{z}=\tan \varnothing -\mathrm{i}$ is _____ .

The principal argument of $z = \tan \alpha + i$ is _____ .

Which of the following is the root of $\log \left(\mathrm{z}\right)=\mathrm{i}\frac{\mathrm{\pi }}{2}$ ?

${(\cosh \mathrm{x} + \sinh \mathrm{x})}^{\mathrm{n}}=$ _____ .

The value of $\tanh (\log \sqrt{7})$ is _____ .

$\cos (\log {\mathrm{i}}^{\mathrm{i}})=$ _____ ; where $\mathrm{i}=\sqrt{-1}$

$\mathrm{i} \log \left(\frac{\mathrm{a}-\mathrm{i}}{\mathrm{a}+\mathrm{i}}\right)=$ _____ ; where $\mathrm{i}=\sqrt{-1}$ .

The value of limit $\underset{\mathrm{z}\to 2\mathrm{i}}{\lim } (3\mathrm{x}+\mathrm{i} {\mathrm{y}}^2)$ is _____ .

The value of limit $\underset{\mathrm{z}\to \infty }{\lim } ( \sqrt{\mathrm{z}-2\mathrm{i}} - \sqrt{\mathrm{z}-\mathrm{i}} )$ is _____ .

The value of limit $\underset{\mathrm{z}\to 1}{\lim } \frac{{\mathrm{z}}^2+\mathrm{z}-2}{\mathrm{z}-1}=$ is _____ .