Complex Numbers Ques 30

$\min _{z \in s}|1-3 i-z|$ is equal to

(a) $\frac{2-\sqrt{3}}{2}$

(b) $\frac{2+\sqrt{3}}{2}$

(c) $\frac{3-\sqrt{3}}{2}$

(d) $\frac{3+\sqrt{3}}{2}$

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Answer:

Correct Answer: 30.(c)

Solution:

Formula:

Equation of a straight line:

  1. $\min _{Z \in}|1-3 i-z|=$ perpendicular distance of point $(1,-3)$

from the line $\quad \sqrt{3} x+y=0 \Rightarrow \frac{|\sqrt{3}-3|}{\sqrt{3+1}}=\frac{3-\sqrt{3}}{2}$



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