z1, z2 are two non-real complex numbers such that (z1/z2)+(z2/z1)=1. Then z1, z2 and the origin

Question

z1, z2 are two non-real complex numbers such that (z1/z2)+(z2/z1)=1. Then z1, z2 and the origin (A) are collinear (B) form right angled triangle (C) form right angle isosceles triangle (D) form an equilateral triangle

Tardigrade Admin · Accepted Answer

If (z1/z2)=z, the given equation becomes z2-z+1=0 i.e., z=-ω and -ω2 or, (z1/z2)=-ω ⇒ z1=-z2 ω O B=|z2-0|=|z2| O A=|z1-0|=|-z2 ω|=|z2||-ω|=|z2| and A B |z2-z1|=|z2+z2 ω| =|z2||1+ω|=|z2||-ω2|=|z2| Thus z1, z2 and origin form an equilateral triangle.

Q. z1​,z2​ are two non-real complex numbers such that z2​z1​​+z1​z2​​=1. Then z1​,z2​ and the origin

are collinear

form right angled triangle

form right angle isosceles triangle

form an equilateral triangle

Q. $z_{1}, z_{2}$ are two non-real complex numbers such that $\frac{z _{1}}{z _{2}} + \frac{z _{2}}{z _{1}} = 1$ . Then $z_{1}, z_{2}$ and the origin