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 numbers 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 in a straight line.
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