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FOR ANY TWO COMPLEX NUMBERS m AND n PROVE THAT arg( mn ) = arg(m)+arg(n)

FOR ANY TWO COMPLEX NUMBERS  m AND n PROVE THAT          arg( mn ) = arg(m)+arg(n) 

Grade:11

1 Answers

Gautham Pai M K
35 Points
9 years ago

Take the complex numbers as z1 and z2 .

We have z1z2=r1eiq1. r2eiq2

=r1r2ei(q1+q2)

=(r1r2)(cos(q1+q2)+isin(q1+q2))

Arg(z1z2)= q1+q2=argz1+argz2

Hence Proved.

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