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  4. If the complex numbers z1, z2, z3, are the vertices of a parallelogram A B C D, then the fourth vertex is

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Q. If the complex numbers $z_1, z_2, z_3$, are the vertices of a parallelogram $A B C D$, then the fourth vertex is

Complex Numbers and Quadratic Equations

Solution:

As $A B C D$ is a parallelogram, mid point of $A C=$ mid point of $B D$
$\Rightarrow \frac{1}{2}\left(z_1+z_3\right)=\frac{1}{2}\left(z_2+z_4\right) $
$\Rightarrow z_4=z_1+z_3-z_2$