# Proving multiplication in complex no

• November 17th 2012, 09:33 AM
Tutu
Proving multiplication in complex no
How to prove |Z1Z2Z3| = |Z1||Z2||Z3| ?

I used Z1 = a+bi
Z2 = c+di
Z3 = e+fi and expanded it all out but I could not simplify the expansion to get |Z1||Z2||Z3|

Am I doing it the right way?

Thank you so so so much!
• November 17th 2012, 09:46 AM
Plato
Re: Proving multiplication in complex no
Quote:

Originally Posted by Tutu
How to prove |Z1Z2Z3| = |Z1||Z2||Z3| ?
I used Z1 = a+bi
Z2 = c+di
Z3 = e+fi and expanded it all out but I could not simplify the expansion to get |Z1||Z2||Z3|

Am I doing it the right way?

I would do it in general by induction.

$\left| {\prod\limits_{k = 1}^n {z_k } } \right| = \prod\limits_{k = 1}^n {\left| {z_k } \right|}$.