prove-that-arg-z1z2-arg-z1-arg-z2-arg-z1-z2-arg-z1-arg-z2-

Question Number 70145 by Scientist0000001 last updated on 01/Oct/19

p r o v e t h a t; a r g (z 1 z 2) = a r g (z 1) + a r g (z 2) .

a r g (z 1 / z 2) = a r g (z 1) - a r g (z 2) .

Answered by MJS last updated on 01/Oct/19

z_{1} = r_{1} e^{i θ_{1}}; z_{2} = r_{2} e^{i θ_{2}}

z_{1} z_{2} = r_{1} r_{2} e^{i (θ_{1} + θ_{2})}

\frac{z_{1}}{z_{2}} = \frac{r_{1}}{r_{2}} e^{i (θ_{1} - θ_{2})}

\arg (r e^{i θ}) = θ

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