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The hyperbola, x2–y2=1 can be represented on the Argand Plane by which of the following equations?

The hyperbola, x2–y2=1 can be represented on the Argand Plane by which of the following equations? Correct Answer z2+z̅2=2

Put z = x+iy. Simplifying z2-z̅2=1 gives 4xyi=1(incorrect); Simplifying z2+z̅2=1 gives 2x2–2y2=1(incorrect); Simplifying z2-z̅2=2, we get 2xyi=1(incorrect); Finally, simplifying z2+z̅2=2 gives x2–y2=1(correct).

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