If z_1 = 1 + 2i,z_2 = 2 + 3i,and z_3 = 3 + 4i | vedclass

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(D) Given the complex numbers: $z_1 = 1 + 2i$,$z_2 = 2 + 3i$,and $z_3 = 3 + 4i$. Calculate the distances between the points: $|z_1 - z_2| = |(1-2) + (

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None of these (Collinear points)

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(D) Given the complex numbers: $z_1 = 1 + 2i$,$z_2 = 2 + 3i$,and $z_3 = 3 + 4i$. Calculate the distances between the points: $|z_1 - z_2| = |(1-2) + (2-3)i| = |-1 - i| = \sqrt{(-1)^2 + (-1)^2} = \sqrt{2}$. $|z_2 - z_3| = |(2-3) + (3-4)i| = |-1 - i| = \sqrt{(-1)^2 + (-1)^2} = \sqrt{2}$. $|z_1 - z_3| = |(1-3) + (2-4)i| = |-2 - 2i| = \sqrt{(-2)^2 + (-2)^2} = \sqrt{8} = 2\sqrt{2}$. Since $|z_1 - z_2| + |z_2 - z_3| = \sqrt{2} + \sqrt{2} = 2\sqrt{2} = |z_1 - z_3|$,the points are collinear and do not form a triangle. Therefore,the correct option is $D$.

If $z_1 = 1 + 2i$,$z_2 = 2 + 3i$,and $z_3 = 3 + 4i$,then $z_1, z_2, z_3$ represent the vertices of a/an:

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