Find the principal value of the following. a. $(2 i)^{(1-2 i)}$ b. $(\mathbf{1}-i)^{(\mathbf{1}+i)}$ c. $(-2)^{-3 i}$ Solve for $z$. Express the value of $z$ in the form $x+i y$. a. $\ln z=-\frac{\pi i}{2}$ b. $\ln z=4-3 i$ c. $\ln z=e-\pi i$ d. $\ln z=0.6+0.4 i$ Show that $\arccos z=-i \ln \left(z+\sqrt{z^{2}-1}\right)$. Find all the values of $z$ that would satisfy the equation $z^{4}=\mathbf{1}-\boldsymbol{i}$.

Show your complete solution.

Public Answer

EU0CIH The First Answerer