1) \(\frac{2+5i}{2-5i} + \frac{2-5i}{2+5i}\) = \(\frac{(2+5i)(2+5i)}{(2-5i)(2+5i)} + \frac{(2-5i)(2-5i)}{(2+5i)(2-5i)}\) = \(\frac{4 + 20i - 25}{4+25} + \frac{4 - 20i - 25}{4+25}\) = \(\frac{-21 + 20i}{29} + \frac{-21 - 20i}{29}\) = \(\frac{-42}{29}\)