1. For which real parameters $a$ does there exist a complex number $z$ such that

$$
|z+\sqrt{2}|=\sqrt{a^{2}-3 a+2} \quad \text { and } \quad|z+i \sqrt{2}|<a ?
$$
1. According to the first condition, $a^{2}-3 a+2 \geq 0$ i.e. $a \leq 1$ or $a \geq 2$, according to the second, $a>0$. From these two conditions, it follows that $0<a \leq 1$ or $a \geq 2$.

Case $a=2$ does not satisfy the condition.

If $0<a<2$, then $a^2 - 3a + 2 < 0$, which contradicts the first condition.

If $a>2$, the condition is satisfied.

Therefore, the solution is $a>2$.

5 points