If z1,z2 and z3 are any three complex numbers, then the fourth vertex of the parallelogram whose three vertices are z1,z2 and z3 taken in order, is:

Question

If z1,z2 and z3 are any three complex numbers, then the fourth vertex of the parallelogram whose three vertices are z1,z2 and z3 taken in order, is: (A)  z1-z2+z3  (B)  z1+z2+z3  (C)  (1/3)(z1-z2+z3)  (D)  (1/3)(z1+z2-z3)

Tardigrade Admin · Accepted Answer

Let z be the fourth vertex of parallelogram, then (z1+z3/2)=(z2+z/2) ⇒ z=z1+z3-z2

Q. If $z_{1}, z_{2}$ and $z_{3}$ are any three complex numbers, then the fourth vertex of the parallelogram whose three vertices are $z_{1}, z_{2}$ and $z_{3}$ taken in order, is:

$z_{1} - z_{2} + z_{3}$

$z_{1} + z_{2} + z_{3}$

$\frac{1}{3} (z_{1} - z_{2} + z_{3})$

$\frac{1}{3} (z_{1} + z_{2} - z_{3})$

$\frac{1}{3} (z_{1} - z_{2} - z_{3})$

Let z be the fourth vertex of parallelogram, then $\frac{z _{1} + z _{3}}{2} = \frac{z _{2} + z}{2}$ $\Rightarrow$ $z = z_{1} + z_{3} - z_{2}$

Q. If z1​,z2​ and z3​ are any three complex numbers, then the fourth vertex of the parallelogram whose three vertices are z1​,z2​ and z3​ taken in order, is:

z1​−z2​+z3​

z1​+z2​+z3​

31​(z1​−z2​+z3​)

31​(z1​+z2​−z3​)

31​(z1​−z2​−z3​)

Let z be the fourth vertex of parallelogram, then 2z1​+z3​​=2z2​+z​ ⇒ z=z1​+z3​−z2​