taiwan-gsat 2020 Q7

taiwan-gsat · Other · ast__math-a 8 marks Complex Numbers Argand & Loci Geometric Properties of Triangles/Polygons from Affixes
In the complex plane, let $O$ be the origin, and let $A$ and $B$ represent points with coordinates corresponding to complex numbers $z$ and $z + 1$ respectively. Given that both points $A$ and $B$ lie on the unit circle centered at $O$, select the correct options.
(1) Line $AB$ is parallel to the real axis
(2) $\triangle OAB$ is a right triangle
(3) Point $A$ is in the second quadrant
(4) $z^{3} = 1$
(5) The point with coordinate $1 + \frac{1}{z}$ also lies on the same unit circle 
In the complex plane, let $O$ be the origin, and let $A$ and $B$ represent points with coordinates corresponding to complex numbers $z$ and $z + 1$ respectively. Given that both points $A$ and $B$ lie on the unit circle centered at $O$, select the correct options.\\
(1) Line $AB$ is parallel to the real axis\\
(2) $\triangle OAB$ is a right triangle\\
(3) Point $A$ is in the second quadrant\\
(4) $z^{3} = 1$\\
(5) The point with coordinate $1 + \frac{1}{z}$ also lies on the same unit circle
Paper Questions
QA QB QC QI QII Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8