Let z - x - iy and w - u - iv be two complex numbers which are connected by the transformation w - z-2z-3- Then the curve in the z plane whose equation is - z-3 - - 1 is transformed into the w plane by

The correct option is D an ellipse |z 3|=1 (x 3)^2+y^2=1 x=3+cosθ y=sinθ w=3+cosθ +i sinθ +2cosθ +isinθ w=3+3cosθ isinθ (u 3 ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Multiples of an Angle

Let z = x +...

Question

Let $z = x + i y$ and $w = u + i v$ be two complex numbers which are connected by the transformation w = $z + \frac{2}{z - 3}$ . Then the curve in the $z$ plane whose equation is $| z - 3 |$ = 1 is transformed into the $w$ plane by

a circle

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a straight line

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an ellipse

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a parabola

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Solution

The correct option is D an ellipse
$| z - 3 | = 1$
$(x - 3)^{2} + y^{2} = 1$
$x = 3 + cos θ$
$y = sin θ$
$w = 3 + cos θ + i sin θ + \frac{2}{cos θ + i sin θ}$
$w = 3 + 3 cos θ - i sin θ$
${(\frac{u - 3}{3})}^{2} + v^{2} = 1$

Which represents an ellipse.

Hence, option C.

Suggest Corrections

Similar questions

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Let z=x+iy and w=u+iv be two complex numbers which are connected by the transformation w = z+2z−3. Then the curve in the z plane whose equation is |z−3| = 1 is transformed into the w plane by

The correct option is D an ellipse|z−3|=1(x−3)2+y2=1x=3+cosθy=sinθw=3+cosθ+isinθ+2cosθ+isinθw=3+3cosθ−isinθ(u−33)2+v2=1Which represents an ellipse.Hence, option C.

Let $z = x + i y$ and $w = u + i v$ be two complex numbers which are connected by the transformation w = $z + \frac{2}{z - 3}$ . Then the curve in the $z$ plane whose equation is $| z - 3 |$ = 1 is transformed into the $w$ plane by

The correct option is D an ellipse
$| z - 3 | = 1$
$(x - 3)^{2} + y^{2} = 1$
$x = 3 + cos θ$
$y = sin θ$
$w = 3 + cos θ + i sin θ + \frac{2}{cos θ + i sin θ}$
$w = 3 + 3 cos θ - i sin θ$
${(\frac{u - 3}{3})}^{2} + v^{2} = 1$

Which represents an ellipse.

Hence, option C.