Points A, B, C in the Argand plane represent complex numbers z1, z2, z3 with z1 = (lambda*z2 + z3)/(lambda + 1), where lambda is a real number. Find the distance of point A from the line through points B and C.

Question

Accepted Answer

0. Since z1 is a weighted average of z2 and z3 with real weights summing to 1, A divides BC internally/externally and lies on line BC, so the perpendicular distance is 0.

Points A, B, C in the Argand plane represent complex numbers z1, z2, z3 with z1 = (lambda*z2 + z3)/(lambda + 1), where lambda is a real number. Find the distance of point A from the line through points B and C.

Solution

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