ILL 1987 Problem 59

It is given that $a_{11}, a_{22}$ are real numbers, that $x_1, x_2, a_{12}, b_1, b_2$ are complex numbers, and that $a_{11}a_{22}=a_{12}\overline{a_{12}}$ (Where $\overline{a_{12}}$ is he conjugate of $a_{12}$ ). We consider the following system in $x_1, x_2$ : $$\overline{x_1}(a_{11}x_1 + a_{12}x_2) = b_1,$$$$\overline{x_2}(a_{12}x_1 + a_{22}x_2) = b_2.$$**(a)Give one condition to make the system consistent.(b)**Give one condition to make $\arg x_1 - \arg x_2 = 98^{\circ}.$ Attachments: