I was studying about complex numbers when I encountered this expression in my notebook, $$|a+b| \geq ||a|-|b||$$ It's different from the two triangle inequalities I already knew i.e. $$|a+b| \leq |a|+|b|$$ and $$|a-b| \geq ||a|-|b||$$ where $a$ and $b$ are any two complex numbers and $|.|$ represents the modulus function.
I couldn't find this inequality on the internet and even tried to prove it myself but don't know how to proceed.
So my question is
- Is this expression right or I had just made some mistake copying it from the board?
- If it's right, how to prove it?
Thanks for help:)