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If z_{1}, z_{2}, z_{3}, z_{4} are complex numbers in an Argand

Question

If $z_{1}, z_{2}, z_{3}, z_{4}$ are complex numbers in an Argand plane satisfying $z_{1} + z_{3} = z_{2} + z_{4}$ . A complex number $^{'} z^{'}$ lies on the line joining $z_{1}$ and $z_{4}$ such that $A r g (\frac{z - z _{2}}{z _{1} - z _{2}}) = A r g (\frac{z _{3} - z _{2}}{z - z _{2}})$ . It is given that $∣ z - z_{4} ∣ = 5, ∣ z - z_{2} ∣ = ∣ z - z_{3} ∣ = 6$ then

area of the triangle formed by

z, z_{1}, z_{2}

37 s q . u ni t s

area of the triangle formed by

z, z_{3}, z_{4}

\frac{15 7}{4} s q . u ni t s

area of the quadrilateral formed by the points

z_{1}, z_{2}, z_{3}, z_{4}

taken in order is

\frac{27 7}{2} s q . u ni t s

area of the quadrilateral formed by the points

z_{1}, z_{2}, z_{3}, z_{4}

taken in order is

\frac{27 7}{4} s q . u ni t s

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Charlotte Discussed

z_{1}, z_{2}, z_{3}, z_{4}

are complex numbers in an Argand plane satisfying

z_{1} + z_{3} = z_{2} + z_{4}

. A complex number

^{'} z^{'}

lies on the line joining

z_{1}

and

z_{4}

such that

A r g (\frac{z - z _{2}}{z _{1} - z _{2}}) = A r g (\frac{z _{3} - z _{2}}{z - z _{2}})

. It is given that

∣ z - z_{4} ∣ = 5, ∣ z - z_{2} ∣ = ∣ z - z_{3} ∣ = 6

then

14 mins ago

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