If |Z| 1, |W| 1, show that |Z-W|²≤(|Z|-|W|)²+(arg Z-arg W)².

Answer: Proved. Write |Z-W|²=(|Z|-|W|)²+4|Z||W|sin² θ 2 where θ=arg Z-arg W. Since |Z||W| 1 and 4sin² θ2≤θ², the bound follows. JEE Advanced 1995 · Complex Numbers — verified solution by the Vidaara Team.

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[JEE Advanced 1995] if z 1 w 1 show that z w 2 z w 2 arg

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If $|Z|\le1,\ |W|\le1$, show that $|Z-W|^2\le(|Z|-|W|)^2+(\arg Z-\arg W)^2$.

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VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 2d ago ▲ 0

Answer: Proved.

Write $|Z-W|^2=(|Z|-|W|)^2+4|Z||W|\sin^2\frac{\theta}2$ where $\theta=\arg Z-\arg W$. Since $|Z||W|\le1$ and $4\sin^2\frac\theta2\le\theta^2$, the bound follows.

JEE Advanced 1995 · Complex Numbers — verified solution by the Vidaara Team.

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