Class 11

Math

Algebra

Complex Number and Quadratic Equations

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 $Arg(z_{1}−z_{2}z−z_{2} )=Arg(z−z_{2}z_{3}−z_{2} )$. It is given that $∣z−z_{4}∣=5,∣z−z_{2}∣=∣z−z_{3}∣=6$ then

- area of the triangle formed by $z,z_{1},z_{2}$ is $37 sq.units$
- area of the triangle formed by $z,z_{3},z_{4}$ is $4157 sq.units$
- area of the quadrilateral formed by the points $z_{1},z_{2},z_{3},z_{4}$ taken in order is $2277 sq.units$
- area of the quadrilateral formed by the points $z_{1},z_{2},z_{3},z_{4}$ taken in order is $4277 sq.units$