(B) Let $z = x + iy$,where $x, y \in \mathbb{R}$.Then $z^2 = (x + iy)^2 = x^2 - y^2 + 2ixy$.The real part of $z^2$ is given by $\text{Re}(z^2) = x^2 -

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(B) Let $z = x + iy$,where $x, y \in \mathbb{R}$.Then $z^2 = (x + iy)^2 = x^2 - y^2 + 2ixy$.The real part of $z^2$ is given by $\text{Re}(z^2) = x^2 - y^2$.Given $\text{Re}(z^2) = 1$,we have $x^2 - y^2 = 1$.This is the standard equation of a rectangular hyperbola.Therefore,the correct option is $B$.

Class 11 Mathematics 4-1.Complex numbers Geometry of complex numbers

Easy

The equation $\text{Re}(z^2) = 1$ represents which of the following?

A
$A$ circle $x^2 + y^2 = 1$
B
$A$ hyperbola $x^2 - y^2 = 1$
C
$A$ parabola or a circle
D
All of the above

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4-1.Complex numbers

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MediumWBJEE 2020

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The equation $\text{Re}(z^2) = 1$ represents which of the following?

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