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If a and b are real numbers between 0 and 1 such that the points z1=a +i ,z2=1+bi and z3=0 form an equilateral triangle,then.ans:a=b=2-√3please explain in step by step to reach above answer |
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Answer» ANSWER Hence ∣z
−z 1
∣=∣z 3
−z 2
∣ a 2 +1=b 2 +1 Or a=±b and z 1 2
+z 2 2
+z 3 2
=z 1
.z 2
+z 3
z 2
+z 3
z 1
a 2 −1+2ai+1−b 2 +2bi=(a−b)+i(1+ab) (a 2 −b 2 )+i(2(a+b))=(a−b)+i(1+ab) Hence 2(a+b)=1+ab Considering b=a, we GET b 2 +1−4b=0 b= 2 4± 16−4
=2± 3
Now |
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