[JEE Advanced 1989] if a b in 0 1 and z 1 a i z 2 1
If $a,b\in(0,1)$ and $z_1=a+i$, $z_2=1+bi$, $z_3=0$ form an equilateral triangle, then $a=$ ____
1 Answer
VAVidaara Admin
✓ Vidaara Team
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· 2d ago
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Answer: $a=2-\sqrt3$ (and $b=2-\sqrt3$).
$|z_1|=|z_2|\Rightarrow a=b$; equilateral $\Rightarrow a^2+1=2(1-a)^2\Rightarrow a^2-4a+1=0\Rightarrow a=2-\sqrt3$ (the root in $(0,1)$).
JEE Advanced 1989 · Complex Numbers — verified solution by the Vidaara Team.
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