Geometrical applications:
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Let z1 and z2 be any two complex numbers showing the points A and B correspondingly in the argand plane. Consider C be the point dividing the line segment AB internally in the ratio m : n i.e AC/BC = m/n, and suppose the complex number related with point C be z.
Consider us rotate the line BC about the point C so that it becomes parallel to CA . The given equation of rotation can be,
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Same as if C(z) divides the sector AB externally in the ratio of m : n, then z = 
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In the particular type, if C(z) is the midpoint of AB then 
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Example: If z1, z2 and z3 ( in anticlockwise sense) shows the vertices of a triangle, calculate the centroid, circumcentre, incentre and the orthocentre of the triangle.
Solution: Suppose G be the centriod and let the line joining A and G meets up the line BC at the point D. We have,
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BD = DC
G divides AD in the ratio of 2 : 1 internally
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Suppose I be the incentre and let the line connecting A and I meet up the line BC at D1. We have
Suppose 'O' be the circum-centre and let the line connecting A and O suppose the line BC at D2.
Let 'P' be the orthocentre and consider the line interconnecting the points A and P cut the line BC and D3.
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