IMO 1987 LL SPA59
It is given that a11, a22 are real numbers, that x1, x2, a12, b1, b2
IMO 1987 LL SPA59
Origin: SPA
Problem
It is given that a11, a22 are real numbers, that x1, x2, a12, b1, b2 are complex numbers, and that a11a22 = a12a12 (where a12 is the conju- gate of a12). We consider the following system in x1, x2: x1(a11x1 + a12x2) = b1, x2(a12x1 + a22x2) = b2. (a) Give one condition to make the system consistent. (b) Give one condition to make arg x1 −arg x2 = 98◦.