The points in the Argand plane represented by | vedclass

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(C) The complex conjugates of the given points in the Argand plane are $A(1-2i)$,$B(2+3i)$,and $C(3+4i)$.Let the coordinates be $A(1, -2)$,$B(2, 3)$,a

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form an obtuse angled triangle

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(C) The complex conjugates of the given points in the Argand plane are $A(1-2i)$,$B(2+3i)$,and $C(3+4i)$.Let the coordinates be $A(1, -2)$,$B(2, 3)$,and $C(3, 4)$.Calculate the squared lengths of the sides:$AB^2 = (2-1)^2 + (3-(-2))^2 = 1^2 + 5^2 = 1 + 25 = 26$$BC^2 = (3-2)^2 + (4-3)^2 = 1^2 + 1^2 = 1 + 1 = 2$$AC^2 = (3-1)^2 + (4-(-2))^2 = 2^2 + 6^2 = 4 + 36 = 40$Since $AB^2 + BC^2 = 26 + 2 = 28$,and $AC^2 = 40$,we observe that $AB^2 + BC^2 Because the sum of the squares of two sides is less than the square of the third side,the angle opposite to the longest side $(AC)$ is obtuse.Therefore,the points form an obtuse angled triangle.Hence,option $(C)$ is correct.

The points in the Argand plane represented by the complex conjugates of $1+2i, 2-3i, 3-4i$:

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