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Question
If the complex numbers z1,z2 and z3 denote the vertices of an isosceles triangle, right angled at z1, then (z1−z2)2+(z1−z3)2 is equal to
If the complex numbers z1,z2 and z3 denote the vertices of an isosceles triangle, right angled at z1, then (z1−z2)2+(z1−z3)2 is equal to
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Solution
The correct option is A 0
Since, the triangleis isosceles and right angled, we can say that (z3−z1)=(z2−z1)(cos90o+isin90o)
⇒(z3−z1)=i(z2−z1)
Squaring bothe sides, we get
(z3−z1)2=−(z2−z1)2
⇒(z3−z1)2+(z2−z1)2=0
Since, the triangleis isosceles and right angled, we can say that
(z3−z1)=(z2−z1)(cos90o+isin90o)
⇒(z3−z1)=i(z2−z1)
Squaring bothe sides, we get
(z3−z1)2=−(z2−z1)2
⇒(z3−z1)2+(z2−z1)2=0
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