= Solution
At the only algebraic normal value $Re=-10$, the generator is a <skew-Hermitian matrix>, so its <matrix exponential> is a <unitary matrix>. Both eigenvalues have zero real part; hence
$$
\boxed{G(t)=1\quad\text{and every nonzero }(x_1(0),x_2(0))\text{ is optimal}.}
$$
There is no distinguished initial amplitude ratio and no perturbation-energy growth. The relations $x_2(0)=ir_\pm x_1(0)$ select the individual orthogonal eigenmodes, but arbitrary nonzero combinations are equally optimal because all singular values are one. If $Re$ is restricted to its physical positive domain, this part has no applicable normal case at all. This resolves the inconsistency in the original printed parameters rather than assuming an unjustified optimal direction.
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