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if z1, z2, z3 and z4 are four complex numbers represented by the vertices of a quadrilateral taken in order such that z1-z4=z2-z3 and amp(z4-z1/z2-z1)=π/2, then the quadrilateral is a(1) Rhombus (2) Square (3)Rectangle (4) A Cyclic Quadrilateral

if z1, z2, z3 and z4 are four complex numbers represented by the vertices of a quadrilateral taken in order such that z1-z4=z2-z3 and amp(z4-z1/z2-z1)=π/2, then the quadrilateral is a(1) Rhombus (2) Square (3)Rectangle (4) A Cyclic Quadrilateral

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
if we read closely, z1, z2, z3, z4 are in order.
then z1-z4 = z2-z3 implies that two opposite side are equal
and further, amp(z4-z1/z2-z1) = \pi/2  implies that
two sides adjacent to each other are perpendicular.
here we are not sure about other two opposite lenghts that those side would be equal to the ech other side or not.
but they will be equal to each other.
hence by this iformation, we can only deduce that it will form a Rectangle

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