If and is real

MATHEMATICS · Single correct · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

z \neq 1

and

\frac{z^2}{z-1}

is real, the point represented by the complex number

z

lies (1) on a circle with centre at the origin (2) either on the real axis or on a circle not passing through the origin (3) on the imaginary axis (4) either on the real axis or on a circle passing through the origin

Related theory

Modulus and Conjugate
Complex Numbers
Complex number operations
Algebra
Argand plane representation
Complex Numbers and Quadratic Equations

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