Answer :

[tex]\begin{gathered} (3\sqrt{7}-5i)^2=(3\sqrt{7}-5i)\cdot(3\sqrt{7}-5i) \\ =3\sqrt{7}\cdot(3\sqrt{7}-5i)-5i\cdot(3\sqrt{7}-5i) \\ =3\cdot3\cdot7-15i\sqrt{7}-15i\sqrt{7}-25 \\ =63-25-30i\sqrt{7} \\ =38-30i\sqrt{7} \end{gathered}[/tex]