Chapter H, Problem 18E

Prove the following properties of complex numbers.

1. (a) $\overline{z+w}=\bar{z}+\bar{w}$
2. (b) $\overline{zw}=\bar{z}\bar{w}$
3. (c) ${\bar{z}}^n={\bar{z}}^n$, where n is a positive integer [Hint: Write z = a + bi, w = c + di.]