Question

# If z=x+iy is a complex number, then the curve represented by Im(z2)=c2, where c is non zero real constant, is a

A
circle
B
straight line
C
ellipse
D
rectangular hyperbola

Solution

## The correct option is D rectangular hyperbolaGiven : z=x+iy Now,  z2=x2−y2+2ixy⇒Im(x2−y2+2xyi)=c2⇒2xy=c2⇒xy=c22   Which is a equation of rectangular hyperbola.

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