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Question

If $$\displaystyle z_{1}= 3+2i,z_{2}= 4+4i,z_{3}= 5+6i,$$ then $$\displaystyle z_{1},z_{2},z_{3}$$ represents the vertices of a/an


A
right angle triangle
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B
equilateral triangle
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C
Isosceles triangle
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D
None of these
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Solution

The correct option is D None of these
Consider
$$z_{1}+z_{3}$$
$$=8+8i$$
$$=2(4+4i)$$
$$=2z_{2}$$
Thus $$z_{1},z_{2},z_{3}$$ lie on a line.
Hence he answer is none of these.

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