If a and c are complex numbers and b is a rea | vedclass

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Question

(A) The equation of the line in the Argand plane is given by $a \bar{z} + \bar{a} z + b = 0$. Let $z = x + iy$ and $a = \alpha + i\beta$. The equation

Vedclass · Accepted Answer

$\frac{|a \bar{c} + \bar{a} c + b|}{2|a|}$

Vedclass · Answer

(A) The equation of the line in the Argand plane is given by $a \bar{z} + \bar{a} z + b = 0$. Let $z = x + iy$ and $a = \alpha + i\beta$. The equation can be rewritten as $a \bar{z} + \overline{a \bar{z}} + b = 0$,which is $2 	ext{Re}(a \bar{z}) + b = 0$. This represents a line in the complex plane. The perpendicular distance $d$ from a point $z_0$ to the line $a \bar{z} + \bar{a} z + b = 0$ is given by the formula $d = \frac{|a \bar{z_0} + \bar{a} z_0 + b|}{2|a|}$. Substituting $z_0 = c$,we get the distance $d = \frac{|a \bar{c} + \bar{a} c + b|}{2|a|}$.

If $a$ and $c$ are complex numbers and $b$ is a real number in the Argand plane,then the perpendicular distance from $c$ to the line $a \bar{z} + \bar{a} z + b = 0$ is

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