Answer :
Answer:
-16 i sqrt(3) + 207
Step-by-step explanation:
Simplify the following:
(2 i sqrt(48) - 3) (-4 i sqrt(12) - 5)
sqrt(12) = sqrt(2^2×3) = 2 sqrt(3):
(2 i sqrt(48) - 3) (-4 i×2 sqrt(3) - 5)
-4×2 = -8:
(2 i sqrt(48) - 3) (-8 i sqrt(3) - 5)
Factor -1 from -8 i sqrt(3) - 5:
(2 i sqrt(48) - 3)×-(8 i sqrt(3) + 5)
sqrt(48) = sqrt(2^4×3) = 2^2 sqrt(3):
-(2 i×2^2 sqrt(3) - 3) (8 i sqrt(3) + 5)
2^2 = 4:
-(2 i×4 sqrt(3) - 3) (8 i sqrt(3) + 5)
2×4 = 8:
-(8 i sqrt(3) - 3) (8 i sqrt(3) + 5)
-(8 i sqrt(3) - 3) = -8 i sqrt(3) + 3:
-8 i sqrt(3) + 3 (8 i sqrt(3) + 5)
(-8 i sqrt(3) + 3) (8 i sqrt(3) + 5) = 3×5 + 3×8 i sqrt(3) + -8 i sqrt(3)×5 + -8 i sqrt(3)×8 i sqrt(3) = 15 + 24 i sqrt(3) - 40 i sqrt(3) + 192 = -16 i sqrt(3) + 207:
Answer: -16 i sqrt(3) + 207
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]