Z₁=10+6i, Z₂=4+6i. If arg Z-Z₁ Z-Z₂ = 4, prove that |Z-7-9i|=3 2.

Answer: Proved. A constant argument 4 between Z-Z₁ and Z-Z₂ makes Z trace an arc of a circle through Z₁,Z₂; its centre is 7+9i and radius 3 2, so |Z-7-9i|=3 2. JEE Advanced 1990 · Complex Numbers — verified solution by the Vidaara Team.

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[JEE Advanced 1990] z 1 10 6i z 2 4 6i if arg z z 1 z

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$Z_1=10+6i,\ Z_2=4+6i$. If $\arg\dfrac{Z-Z_1}{Z-Z_2}=\dfrac\pi4$, prove that $|Z-7-9i|=3\sqrt2$.

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

Answer: Proved.

A constant argument $\frac\pi4$ between $Z-Z_1$ and $Z-Z_2$ makes $Z$ trace an arc of a circle through $Z_1,Z_2$; its centre is $7+9i$ and radius $3\sqrt2$, so $|Z-7-9i|=3\sqrt2$.

JEE Advanced 1990 · Complex Numbers — verified solution by the Vidaara Team.

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