I talked to my professor and they said that it can be disproven using an example, specifically using a picture to explain why it statement is false. Can anyone help me out?
2026-03-25 03:07:33.1774408053
Prove or disprove that Arg(zw)=Arg(z)+Arg(w)
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Assuming the version that lives in $(-\pi , \pi]$, "Arg" tells you how far you are from the positive real axis, angle-wise. The product of two complex numbers can be much closer than the factors originally were. Try drawing a unit circle.