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If a ,b,c, and u,v,w are complex numbers...

If a ,b,c, and u,v,w are complex numbers representing the vertices of two triangle such that they are similar, then prove that `(a-c)/(a-b) =(u-w)/(u-v)`

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To prove that \(\frac{a-c}{a-b} = \frac{u-w}{u-v}\) for complex numbers \(a, b, c\) and \(u, v, w\) representing the vertices of two similar triangles, we will follow these steps: ### Step 1: Understand the Similarity of Triangles Given that triangles \(ABC\) and \(UVW\) are similar, we know that the ratios of the lengths of corresponding sides are equal. This means: \[ \frac{AB}{PQ} = \frac{AC}{PR} = \frac{BC}{QR} \] where \(AB\), \(AC\), and \(BC\) are the lengths of the sides of triangle \(ABC\) and \(PQ\), \(PR\), and \(QR\) are the lengths of the sides of triangle \(UVW\). ...
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