- #1
josueortega
- 8
- 0
Hi everyone,
I have a question on Rudin's proof of Theorem 1.33 part e. Here he prove the following statement:
The absolute value of z+w is equal or smaller than the absolute value of z plus the absolute value of w -Yes, is the triangle inequality, where z and w are both complex numbers-
|z+w| $\leqslant$ |z| + |w|
In the proof, the key is that he points out that
$$2Re(z\overline{w}) \leqslant 2|z\overline{w}|$$
which obviously implies that
$$Re(z\overline{w}) \leqslant |z\overline{w}|$$
Why is that so? How does he knows this inequality is satified? If you can help me I would appreciate it a lot.
I have a question on Rudin's proof of Theorem 1.33 part e. Here he prove the following statement:
The absolute value of z+w is equal or smaller than the absolute value of z plus the absolute value of w -Yes, is the triangle inequality, where z and w are both complex numbers-
|z+w| $\leqslant$ |z| + |w|
In the proof, the key is that he points out that
$$2Re(z\overline{w}) \leqslant 2|z\overline{w}|$$
which obviously implies that
$$Re(z\overline{w}) \leqslant |z\overline{w}|$$
Why is that so? How does he knows this inequality is satified? If you can help me I would appreciate it a lot.