The figure in the complex plane given by 10zz¯-3z^2+z¯^2+4iz^2-z¯^2=0

Correct answer: (A) a straight line. 10zz¯-3(z+z¯)^2-2zz¯+4i((z+z¯)(z-z¯))=0 Let z=x+iy 10x^2+y^2-34x^2-2x^2-2y^2+4i(2x(2iy))=0 ⇒4x^2+16y^2-16xy=0 ⇒x^2-4xy+4y^2=0 ⇒(x-2y)^2=0⇒x=2y ∴ straight line

Q48 / 91 · KVPY 2020 (SB/SX) · Mathematics

The figure in the complex plane given by
$10 z \bar{z} - 3 (z^{2} + {\bar{z}}^{2}) + 4 i (z^{2} - {\bar{z}}^{2}) = 0$

Correct answer
A
a straight line
B
a circle
C
a parabola
D
an ellipse

Solution

$10 z \bar{z} - 3 ((z + \bar{z})^{2} - 2 z \bar{z}) + 4 i ((z + \bar{z}) (z - \bar{z})) = 0$
Let $z = x + i y$

$10 (x^{2} + y^{2}) - 3 (4 x^{2} - 2 x^{2} - 2 y^{2}) + 4 i (2 x (2 i y)) = 0$
$\Rightarrow 4 x^{2} + 16 y^{2} - 16 x y = 0$
$\Rightarrow x^{2} - 4 x y + 4 y^{2} = 0$
$\Rightarrow (x - 2 y)^{2} = 0 \Rightarrow x = 2 y$
$∴$ straight line

Hence, the correct answer is option: 'A'.

The figure in the complex plane given by 10zz¯-3z2+z¯2+4iz2-z¯2=0

Solution

More Complex Number Questions

The figure in the complex plane given by
$10 z \bar{z} - 3 (z^{2} + {\bar{z}}^{2}) + 4 i (z^{2} - {\bar{z}}^{2}) = 0$