Complex numbers (1 Viewer)

[lugana]

Hi guys,

question from complex numbers.

please anyone tell me the proof

if z=z₁×z₂ then |z|=|z₁|×|z₂| (modulus) , if z=z₁/z₂ then |z|=|z₁|/|z₂|


and

if |z|=|z₁|×|z₂| then z=z₁×z₂ , if |z|=|z₁|/|z₂| then z=z₁/z<sub>2


Thanks!</sub>

 

[Carrotsticks]

The algebraic argument (though a bit tedious) would be to define:



Then to find the modulus of each of them and prove LHS = RHS etc.

 

[lugana]

Thank you! I did the first two prooves but couldn't do the last two... Will you tell me again ?

And is it necessary to do this proof every time in my solution? Or can I use them straight?