Complex Numbers Thereoms (1 Viewer)

[HSC2014]

I've been able to prove that |z1z2| = |z1||z2| and coinciding that arg z1z2 = arg z1 + arg z2

However what about |z1/z2| and arg z1/z2? (arg z1/z2 = arg z1 - arg z2) I'd assume the proofs are very similar since the division function is essentially the multiplication function in inverse however I still cannot get it.

How do I go about proving these?

 

[braintic]

See Attachment: View attachment z1 div z2.pdf

 

[HeroicPandas]

 

[braintic]

But going from your 2nd to 3rd line uses the result you are trying to prove.

 

[HSC2014]

See Attachment: View attachment 28548

Thank you! Perfect

 

[HeroicPandas]

But going from your 2nd to 3rd line uses the result you are trying to prove.

yes u are correct! that was an idiotic proof