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TS EAMCET · Maths · Complex Number

If the four points \(A, B, C, D\) in the Argand plane represented respectively by the complex numbers \(2+i, 4+3 i, 2+5 i, 3 i\) lie on a circle, then the centre of the circle is

  1. A \(1+2 i\)
  2. B \(3+2 i\)
  3. C \(3+4 i\)
  4. D \(2+3 i\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(2+3 i\)

Step-by-step Solution

Detailed explanation

Four points \(A, B, C, D\) on a Circle are \((2,1),(4,3),(2,5),(0,3)\) Slope of \(A B=\frac{3-1}{4-2}=\frac{2}{2}=1\) Slope of \(B C=\frac{5-3}{2-4}=-1\) \(A B C\) is a right angle \(\Delta\) \(\therefore\) Centre of circle is mid-point of \(A C\) i.e.,…