Hello, Nrt!
I believe there is a typo in #2.
2) Show that if
then: .
Since is in the unit circle centered at the origin.
. .
Code:| o o o o | z o o | ∆ o o *| * o * | * o * | * o - B∆ - - - - + - - - - ∆A - o | o | o | o o | o o | o o o o |
From the triangle inequality: .
. . Therefore: .
It is the exact same proof for complex numbers as for real real.
You must realize that is just a real number.
The triangle inequality holds for complex numbers: .
So you can get .
At this point you have nothing but real numbers and you use this fact.
If and then or .
See you let and noting that .