For this case we must simplify the following expression:
[tex](-3 + 2i \sqrt {48}) (- 5-4i \sqrt {12})[/tex]
Rewriting:
[tex](-3 + 2i \sqrt {4 ^ 2 * 3}) (- 5-4i \sqrt {2 ^ 2 * 3}) =\\(-3 + 2 * 4i \sqrt {3}) (- 5-4 * 2i \sqrt {3}) =\\(-3 + 8i \sqrt {3}) (- 5-8i \sqrt {3}) =[/tex]
We apply distributive property:
[tex]- * - = +\\- * + = -\\15 + 24i \sqrt {3} -40i \sqrt {3} - (8i \sqrt {3}) ^ 2 =\\15 + 24i \sqrt {3} -40i \sqrt {3} -64i ^ 2 * 3 =[/tex]
We have to[tex]i ^ 2 = -1[/tex]:
[tex]15 + 24i \sqrt {3} -40i \sqrt {3} + 192 =[/tex]
Adding similar terms:
[tex]207-16i \sqrt {3}[/tex]
Answer:
[tex]207-16i \sqrt {3}[/tex]
