The curve represented by Im(z²) = k, where k is a non-zero real number, is
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Given : curve represented by Im(z²) = k, where k is a non-zero real number,
To Find : curve
Solution:
z = x + iy
z² = (x + iy)²
=> z² =x² - y² + 2xyi
Im (z²) = 2xy
Im(z²) = k
=> 2xy = k
=> xy = k/2
=> xy = c
this is an equation of hyperbola
This is also called rectangular hyperbola
as asymptotes are x axis and y axis
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