(B) The given equation is $\overline{b}z + b\overline{z} = c$. Let $z = x + iy$ and $b = b_1 + ib_2$,where $x, y, b_1, b_2 \in \mathbb{R}$. Substituti

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(B) The given equation is $\overline{b}z + b\overline{z} = c$. Let $z = x + iy$ and $b = b_1 + ib_2$,where $x, y, b_1, b_2 \in \mathbb{R}$. Substituting these into the equation,we get: $(b_1 - ib_2)(x + iy) + (b_1 + ib_2)(x - iy) = c$ $(b_1x + ib_1y - ib_2x + b_2y) + (b_1x - ib_1y + ib_2x + b_2y) = c$ $2b_1x + 2b_2y = c$. This is a linear equation in $x$ and $y$ of the form $Ax + By + C = 0$,which represents a straight line.

Class 11 Mathematics 1 Complex Numbers and Quadratic Equations: Complex Numbers Geometry of complex numbers

Medium

The equation $\overline{b}z + b\overline{z} = c$,where $b$ is a non-zero complex constant and $c$ is real,represents:

A
$A$ circle
B
$A$ straight line
C
$A$ parabola
D
None of these

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Chapter

1 Complex Numbers and Quadratic Equations: Complex Numbers

Subtopic

Geometry of complex numbers

Let $x_1, x_2, x_3, x_4$ be the roots of the equation $4x^4 + 8x^3 - 17x^2 - 12x + 9 = 0$. If $(4+x_1^2)(4+x_2^2)(4+x_3^2)(4+x_4^2) = \frac{125}{16}m$,then the value of $m$ is:

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If $z = \sqrt{2} - i\sqrt{2}$ is rotated through an angle $45^{\circ}$ in the anti-clockwise direction about the origin,then the coordinates of its new position are

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$PQ$ and $PR$ are two infinite rays. $QAR$ is an arc. $A$ point lying in the shaded region,excluding the boundary,satisfies:

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If $z_1 = 10 + 6i$,$z_2 = 4 + 6i$ and $z$ is any complex number such that the argument of $\frac{z - z_1}{z - z_2}$ is $\frac{\pi}{4}$,then

MediumAP EAMCET 2024

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The values of $z$ for which $|z + i| = |z - i|$ are

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The equation $\overline{b}z + b\overline{z} = c$,where $b$ is a non-zero complex constant and $c$ is real,represents:

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Let $x_1, x_2, x_3, x_4$ be the roots of the equation $4x^4 + 8x^3 - 17x^2 - 12x + 9 = 0$. If $(4+x_1^2)(4+x_2^2)(4+x_3^2)(4+x_4^2) = \frac{125}{16}m$,then the value of $m$ is:

If $z = \sqrt{2} - i\sqrt{2}$ is rotated through an angle $45^{\circ}$ in the anti-clockwise direction about the origin,then the coordinates of its new position are

$PQ$ and $PR$ are two infinite rays. $QAR$ is an arc. $A$ point lying in the shaded region,excluding the boundary,satisfies:

If $z_1 = 10 + 6i$,$z_2 = 4 + 6i$ and $z$ is any complex number such that the argument of $\frac{z - z_1}{z - z_2}$ is $\frac{\pi}{4}$,then

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