If three complex numbers are in ap then they lie on

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Solution

2Z₂=Z₁+Z₃
2(x₂+iy₂)=(x₁+x₃)+i(y₁+y₃)
comparing real and imaginary parts
x₂=x₁+x₃/2 , y₂=y₁+y₃/2
Z₂ is midpoint of Z₁andZ₃
they lie on a st.line

Then they lie in same plane,line

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