InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If `z=r e^(itheta)`, then prove that `|e^(i z)|=e^(-r s inthetadot)` |
|
Answer» `z = re^(i0) = r (cos theta + i sin theta)` `rArr iz = ir (cos theta + i sin theta)` `=- rsin theta + ir cos theta` `rArr e^(1z) = e^((-rsin theta+ ir cos theta))` `= e^((-rsin theta)) e^((ri cos theta))` `rArr |e^(iz)|=|e^(-rsin theta)||e^(r icos theta)|` `= e^((- r sin theta))|e^(ialpha)|," ""where"alpha = r cos theta` `= e^(-rsin theta)` |
|