AP EAMCET · Maths · Complex Number
If \(\mathrm{z}_1, \mathrm{z}_2, \mathrm{z}_3\) are the vertices of an equilateral triangle and \(\mathrm{z}\) is its circum centre, then
- A \(\frac{\left|z-z_1\right|}{\left|z-z_2\right|}=\frac{\left|z-z_3\right|}{\left|z-z_1\right|}\)
- B \(\left|z-z_1\right|+\left|z-z_2\right|+\left|z-z_3\right|=0\)
- C \(\frac{\left|z-z_1\right|}{\left|z-z_2\right|}=\left|z-z_3\right|\)
- D \(\frac{\left|z-z_1\right|+\left|z-z_2\right|}{\left|z-z_3\right|}=1\)
Answer & Solution
Correct Answer
(A) \(\frac{\left|z-z_1\right|}{\left|z-z_2\right|}=\frac{\left|z-z_3\right|}{\left|z-z_1\right|}\)
Step-by-step Solution
Detailed explanation
Given that \(z_1, z_2, z_3\) are the vertices of an equilateral triangle and \(\mathrm{z}\) is its circumcentre.…
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