Find the complex number $p+qi$.

Question

$a, b, c$ are different complex numbers and they satisfy the following:

$$\frac{a}{1-b}=\frac{b}{1-c}=\frac{c}{1-a}=p+qi.$$

Find the values for $p$ and $ q$.

I have found out that $(a-b)^2+(b-c)^2+(c-a)^2=0$

Answer 1

Hint: Let $p+qi = z$, then $ z = a + zb = b + z c = c + za $.

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