MathDB

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}.

Problem Statement