Find all \(z\) such that \(\cos z=2\), or explain why there are none. You will need to consider \(\cos (x+i y)\) and equate real and imaginary parts of the resulting expression similar to Problem 5.

Data from Problem 5

Show that \(\sin (x+i y)=\sin x \cosh y+i \cos x \sinh y\) using trigonometric identities and the exponential forms of these functions.