If the four points A, B, C, D in the Argand p | vedclass

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(D) The four points $A, B, C, D$ in the Argand plane correspond to the coordinates $(2, 1), (4, 3), (2, 5), (0, 3)$.First,calculate the slopes of the

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$2+3i$

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(D) The four points $A, B, C, D$ in the Argand plane correspond to the coordinates $(2, 1), (4, 3), (2, 5), (0, 3)$.First,calculate the slopes of the sides:Slope of $AB = \frac{3-1}{4-2} = \frac{2}{2} = 1$.Slope of $BC = \frac{5-3}{2-4} = \frac{2}{-2} = -1$.Since the product of the slopes is $1 	imes (-1) = -1$,the angle $\angle ABC = 90^\circ$.Similarly,$\angle BCD = 90^\circ$,$\angle CDA = 90^\circ$,and $\angle DAB = 90^\circ$.Thus,the quadrilateral $ABCD$ is a rectangle.In a rectangle inscribed in a circle,the diagonals are diameters of the circle.The centre of the circle is the midpoint of the diagonal $AC$.Midpoint of $AC = \left(\frac{2+2}{2}, \frac{1+5}{2}ight) = (2, 3)$.In complex form,this is $2+3i$.

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

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