1. **State the problem:** Simplify the expression $$(\sqrt{22} - \sqrt{3}i) + (\sqrt{22} + \sqrt{3}i).$$ 2. **Recall the formula and rules:** When adding complex numbers, add the real parts together and the imaginary parts together. 3. **Apply addition:** $$ (\sqrt{22} - \sqrt{3}i) + (\sqrt{22} + \sqrt{3}i) = (\sqrt{22} + \sqrt{22}) + (-\sqrt{3}i + \sqrt{3}i).$$ 4. **Simplify real and imaginary parts:** $$ 2\sqrt{22} + 0 = 2\sqrt{22}.$$ 5. **Final answer:** $$\boxed{2\sqrt{22}}.$$