Question

I. If $\frac{z_1}{z_2}+\frac{z_2}{z_1}=1$ then origin $z_1,z_2$ form equilateral triangle.
II. $z_1^2+z_2^2+z_3^2=3z_0^2$ then $z_0$ is circumcentre of equilateral triangle with the vertices $z_1,z_2,z_3$.

• A. I and II are true
• B. I is true, II is false
• C. I false, II is true
• D. I is false, II is false

Answer 1

Answer: (A)

I and II are true

Statement$\left(1\right)$

If $z_1\&z_2$ are two ordered pairs that form equilateral triangle then ${z_1}^2+{z_2}^2=z_1{z}_2$

Therefore $\frac{z_1}{z_2}+\frac{z_2}{z_1}=1$ (True)

Statement(2)

Let $z_1,z_2\&z_3$ are three ordered pairs that form a triangle with the points $(x_1,y_1),(x_2,y_2),(x_{13},y_3)z_1=(x_1,y_1);z_2=(x_2,y_2);z_3=(x_{13},y_3)z_0=\sqrt{x^2+y^2}then{z_1}^2+{z_2}^2+{z_3}^2={3z_0}^2$

Therefore both statements are true