Unit groups and Iwasawa lambda invariants of some multiquadratic number fields

Let $$q_1$$ and $$q_2$$ be two prime integers such that $$q_1\equiv 7\pmod 8$$ and $$q_2\equiv 3\pmod 8$$ . In this work we determine the unit groups of the fields $$\mathbb {L}={\mathbb {Q}}(\sqrt{q_1}, \sqrt{q_2}, \sqrt{2},i)$$ and $$\mathbb {L}^+={\mathbb {Q}}(\sqrt{q_1}, \sqrt{q_2}, \sqrt{2})$$ . Furthermore, as applications we compute the Iwasawa $$\lambda$$ -invariant for some multiquadratic number fields of the form $$F={\mathbb {Q}}(\sqrt{q_1}, \sqrt{q_2},i)$$ .