R( z^2 ) = 1 is represented by - Vidyadip

MCQ

$R({z^2}) = 1$ is represented by

A
circle ${x^2} + {y^2} = 1$
✓
The hyperbola ${x^2} - {y^2} = 1$
C
Parabola or a circle
D
All the above

✓

Answer

Correct option: B.

The hyperbola ${x^2} - {y^2} = 1$

b
(b) $z = (x + iy)$==> ${z^2} = {x^2} - {y^2} + 2ixy$
==> ${\mathop{\rm Re}\nolimits} ({z^2}) = 1$

==> ${x^2} - {y^2} = 1$, which is a hyperbola.

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