Hi, How would you show that for all z,w in the complex no. that ||z|-|w|| is less than or equal to |z-w| and that if the sequence z_n tends to w it implies that |z_n| tends to |w|.

They probably follow a similar pattern to the proof for real numbers but I'm unsure about bits of it.

It also asks how to show that for theta in the reals, ||z|-|w|| is less than or equal to |z+we^(itheta)| and hence that ||z|-|w|| = min{|z +we^(itheta)| : theta in reals}

I'm not even sure if we've done this in class.

thanks for any help