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8

Part of 2017 Math Prize for Girls Problems

Problems(1)

Math Prize 2017 Problem 8

Source:

9/26/2017
Let cc be a complex number. Suppose there exist distinct complex numbers rr, ss, and tt such that for every complex number zz, we have (z−r)(z−s)(z−t)=(z−cr)(z−cs)(z−ct). (z - r)(z - s)(z - t) = (z - cr)(z - cs)(z - ct). Compute the number of distinct possible values of cc.
Math Prize for Girlscomplex numbers