Solutions to Exercises

1. z*zbar=|z|^2

2. z+zbar=2Re(z)
z-zbar=2iIm(z)

3. |zw|=|z| |w|

4. |z/w|=|z|/|w|

5. Trivial

6. |Re(z)|^2 + |Im(z)|^2 = |z|^2
Re(z) <= |z|
Im(z) <= |z|

7. |z+w| <= |z|+|w|

8. | |z| - |w| |<= |z-w| <= |z| + |w|