(A) Let $a = x + iy$,where $x, y \in \mathbb{R}$. Then $\bar{a} = x - iy$. Substituting these into the given equation $\bar{a} + a + b = 0$: $(x - iy)

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(A) Let $a = x + iy$,where $x, y \in \mathbb{R}$. Then $\bar{a} = x - iy$. Substituting these into the given equation $\bar{a} + a + b = 0$: $(x - iy) + (x + iy) + b = 0$ $2x + b = 0$ $x = -\frac{b}{2}$ Since $b$ is a real number,$-\frac{b}{2}$ is a constant. The equation $x = \text{constant}$ represents a vertical straight line in the complex plane.

Class 11 Mathematics 4-1.Complex numbers Geometry of complex numbers

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If $a$ is a complex number and $b$ is a real number,then the equation $\bar{a}+a+b=0$ represents $a$ as a locus of points in the complex plane,which is a:

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straight line
B
parabola
C
circle
D
hyperbola

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If $a$ is a complex number and $b$ is a real number,then the equation $\bar{a}+a+b=0$ represents $a$ as a locus of points in the complex plane,which is a:

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