Let z1 and z2 be distinct complex numbers. Show that the locus of poi.pdf
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The document demonstrates that the locus of points formed by the expression tz1 + (1 - t)z2, with distinct complex numbers z1 and z2, gives the direction ratios of the line joining these points. The equation z2 + t(z1 - z2) represents the line between z1 and z2 as t varies. Specific values of t (0 and 1) correspond to the points z2 and z1, respectively, illustrating the linear transition between the two points.
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Let z1 and z2 be distinct complex numbers. Show that the locus of poi.pdf
- 1. Let z1 and z2 be distinct complex numbers. Show that the locus of points tz1 + (1 - t)z2, - infinity Solution tz1+z2-tz2 = t(z1-z2)+z2 z1-z2 gives the direction ratios of the line joining z1 and z2. Thus the equation z2+t(z1-z2) gives the equation of the line passing through z1 and z2. for various values of t. ----------------------------------------------- If t =0, equation will be z2 i.e. a single point z2. If t=1, equation will be z1 a single point z1. When t varies from 0 to 1 it slowly extends from the point z2 and ends in z1.