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-√3
please explain in step by step to reach above answer
Answers
Answered by
1
Answer:
ANSWER
Hence
∣z
3
−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
0<a<1 and 0<b<1
Hence
a=b=2−
3
Similar questions