Question

(-3+2iroot48)(-5-4iroot12)

Answer 1

For this case we must simplify the following expression:

$(-3 + 2i \sqrt {48}) (- 5-4i \sqrt {12})$

Rewriting:

$(-3 + 2i \sqrt {4 ^ 2 * 3}) (- 5-4i \sqrt {2 ^ 2 * 3}) =\\(-3 + 2 * 4i \sqrt {3}) (- 5-4 * 2i \sqrt {3}) =\\(-3 + 8i \sqrt {3}) (- 5-8i \sqrt {3}) =$

We apply distributive property:

$- * - = +\\- * + = -\\15 + 24i \sqrt {3} -40i \sqrt {3} - (8i \sqrt {3}) ^ 2 =\\15 + 24i \sqrt {3} -40i \sqrt {3} -64i ^ 2 * 3 =$

We have to$i ^ 2 = -1$:

$15 + 24i \sqrt {3} -40i \sqrt {3} + 192 =$

Adding similar terms:

$207-16i \sqrt {3}$

Answer:

$207-16i \sqrt {3}$