Question

The hyperbola, x^2–y^2=1 can be represented on the Argand Plane by which of the following equations?

(a) z^2-z̅^2=1

(b) z^2+z̅^2=1

(c) z^2-z̅^2=2

(d) z^2+z̅^2=2

I got this question by my school teacher while I was bunking the class.

This key question is from Complex Conjugates in section Complex Numbers of Engineering Mathematics

Answer 1

The correct answer is (d) z^2+z̅^2=2

Best explanation: Put z = x+iy. Simplifying z^2-z̅^2=1 gives 4xyi=1(incorrect);

Simplifying z^2+z̅^2=1 gives 2x^2–2y^2=1(incorrect);

Simplifying z^2-z̅^2=2, we get 2xyi=1(incorrect);

Finally, simplifying z^2+z̅^2=2 gives x^2–y^2=1(correct).