If Q is real and z1,z2 are connected by z21+z22+2z1z2cosθ=0, then triangle with vertices 0,z1 and z2 is
A
equilateral
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B
right-angled
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C
isosceles
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D
None of these
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Solution
The correct option is A isosceles Given, z21+z22+2z1z2cosθ=0 ⇒(z1z2)2+2(z1z2)cosθ+1=0 ⇒(z1z2+cosθ)2=−(1−cos2θ)=−sin2θ ⇒z1z2=−cosθ±isinθ ⇒∣∣∣z1z2∣∣∣=√(−cosθ)2+(sinθ)2=1 ⇒|z1|=|z2| ⇒|z1−0|=|z2−0| Thus, triangle with vertices 0,z1,z2 is isosceles.