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If z1, z2, z3 are three nonzero complex ...

If `z_1, z_2, z_3` are three nonzero complex numbers such that `z_3=(1-lambda)z_1+lambdaz_2 w h e r e lambda in R-{0},` then prove that points corresponding to `z_1, z_2a n dz_3` are collinear .

Text Solution

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`z_(3) = (1-lambda)z_(1) +z_(2)`
` = ((1-lambda)z_(1)+lambdaz_(2))/(1-lambda+lambda)`
Hence, `z_(3)` divides the line joining `A(z_(1))` and `B(z_(2))` in the ratio
`lambda:(1-lambda)`. Thus, the given points are collinera.
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