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Math Help - Proving multiplication in complex no

  1. #1
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    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!
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  2. #2
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    Re: Proving multiplication in complex no

    Quote Originally Posted by Tutu View Post
    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|} .
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