(Solved):           please answer all 5 questions What is \( \cos (i)^{2 ...

 

 

 

 

 
please answer all 5 questions

What is \( \cos (i)^{2} \) ? A. \( 2.3811 \mathrm{i} \) B. \( -2.3811 \) C. - 2.3811i D. - \( 2.3811 \) E. None of the above Find the value of \( \sin \left(\frac{\pi}{4}(1+i)\right) \) A. \( \frac{\sqrt{2}}{2}\left(\cosh \left(\frac{\pi}{4}\right)-i \sinh \left(\frac{\pi}{4}\right)\right) \) B. \( \frac{\sqrt{2}}{2}\left(i \cosh \left(\frac{\pi}{4}\right)+\sinh \left(\frac{\pi}{4}\right)\right) \) C. \( \left(\cosh \left(\frac{\pi}{4}\right)+i \sinh \left(\frac{\pi}{4}\right)\right) \) D. \( \frac{\sqrt{2}}{2}\left(\cosh \left(\frac{\pi}{4}\right)+\sinh \left(\frac{\pi}{4}\right)\right) \) E. None of the above What does \( e^{z+\pi i} \) equal? A. \( -e^{-z} \) B. \( e^{z} \) C. \( e^{-z} \) D. \( -e^{z} \) E. None of the above What does \( e^{2+\pi i} \) equal? A. 1 B. \( e^{2} \) C. \( i e^{2} \) D. \( -1 \) E. \( -e^{2} \) F. None of the above Find all values of \( z \) such that \( e^{z}=-2 \) \[ \begin{array}{l} \quad \text { A. } \ln (2)+(2 n+1) \pi i \\ n \in Z \end{array} \] B. \( \ln (2)+(2 n) \pi i \) \( n \in Z \) c. \( \ln (2)+\pi i \) D. \( \ln (2)+(2 n+2) \pi i \) \( n \in Z \) E. None of the above