1. Tardigrade
  2. Question
  3. Mathematics
  4. The curve represented by Im(z2) = λ (λ ≠ 1) is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The curve represented by $Im(z^2) = \lambda (\lambda \ne 1)$ is

Complex Numbers and Quadratic Equations

Solution:

Let $z = x + iy$
$\therefore z^2 = (x^2 - y^2) + 2ixy$
$\therefore Im(z^2) = 2xy$
$\Rightarrow 2xy = \lambda $
$\Rightarrow xy = \lambda'$
which is a rectangular hyperbola.