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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


Your Answer
A
circle
Your Answer
B
straight line
Your Answer
C
ellipse
Correct Answer
D
rectangular hyperbola

Solution

The correct option is D rectangular hyperbola
Given : z=x+iy
Now, 
z2=x2y2+2ixyIm(x2y2+2xyi)=c22xy=c2xy=c22
 
Which is a equation of rectangular hyperbola.

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