A) a circle in the complex plane
B) a straight line in the complex plane
C) a parabola in the complex plane
D) none of these
Correct Answer: B
Solution :
Let\[{{z}_{1}},{{z}_{2}},{{z}_{3}}\]be three complex number in A.P. then\[2{{z}_{2}}={{z}_{1}}+{{z}_{3}}\] thus the complex number\[{{z}_{2}}\]is the mid-point of the line joining the points\[{{z}_{1}}\]and\[{{z}_{3}}\]. So the three points\[{{z}_{1}},{{z}_{2}}\]and\[{{z}_{3}}\]are on a straight line.
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