If z - x - iy is a complex number- then the curve represented by Im z 2- c 2- where c is non zero real constant- is aA- circleB- straight lineC- ellipseD- rectangular hyperbola

Given : z=x+iy Now, nbsp; z^2 = nbsp;x^2 y^2+2ixy ⇒ Im(x^2 y^2+2xyi)=c^2 ⇒ 2xy = c^2 ⇒ xy = c^22 nbsp; Which is a equation of rectangular hyperbola. ...

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Standard XII

Mathematics

Algebra of Complex Numbers

If z = x + iy...

Question

If $z = x + i y$ is a complex number, then the curve represented by $I m (z^{2}) = c^{2}$ , where $c$ is non zero real constant, is a

circle

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straight line

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ellipse

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rectangular hyperbola

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Solution

The correct option is D rectangular hyperbola
Given : $z = x + i y$
Now,
$z^{2} = x^{2} - y^{2} + 2 i x y \Rightarrow I m (x^{2} - y^{2} + 2 x y i) = c^{2} \Rightarrow 2 x y = c^{2} \Rightarrow x y = \frac{c^{2}}{2}$

Which is a equation of rectangular hyperbola.

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Algebra of Complex Numbers

Standard XII Mathematics

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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

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.

If $z = x + i y$ is a complex number, then the curve represented by $I m (z^{2}) = c^{2}$ , where $c$ is non zero real constant, is a

The correct option is D rectangular hyperbola
Given : $z = x + i y$
Now,
$z^{2} = x^{2} - y^{2} + 2 i x y \Rightarrow I m (x^{2} - y^{2} + 2 x y i) = c^{2} \Rightarrow 2 x y = c^{2} \Rightarrow x y = \frac{c^{2}}{2}$

Which is a equation of rectangular hyperbola.