(B) The given equation is $\frac{|3z - i|}{|4z - 2 + 3i|} = K$. We can rewrite this as $\frac{3|z - i/3|}{4|z - (2-3i)/4|} = K$. This simplifies to $\

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(B) The given equation is $\frac{|3z - i|}{|4z - 2 + 3i|} = K$. We can rewrite this as $\frac{3|z - i/3|}{4|z - (2-3i)/4|} = K$. This simplifies to $\frac{|z - i/3|}{|z - (1/2 - 3i/4)|} = K \cdot \frac{4}{3}$. The locus of points $z$ satisfying $\frac{|z - z_1|}{|z - z_2|} = \lambda$ is a straight line if and only if $\lambda = 1$. Therefore,$K \cdot \frac{4}{3} = 1$,which gives $K = \frac{3}{4}$.

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

If $\frac{|3z - i|}{|4z - 2 + 3i|} = K$ $(K \in \mathbb{R}^+)$ represents a straight line,then the value of $K$ is:

A
$\frac{4}{3}$
B
$\frac{3}{4}$
C
$1$
D
None of these

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4-1.Complex numbers

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DifficultIIT 2002

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DifficultJEE MAIN 2019

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The maximum value of the modulus of $e^{z^2}$ on the set $\{z \in \mathbb{C} : 0 \leq \operatorname{Re}(z) \leq 1, 0 \leq \operatorname{Im}(z) \leq 1\}$ is

MediumAP EAMCET 2018

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If $\frac{|3z - i|}{|4z - 2 + 3i|} = K$ $(K \in \mathbb{R}^+)$ represents a straight line,then the value of $K$ is:

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