Question

Help is appreciated! Thanks!

I really need these answers explained!!

1) Simplify
-4i√-48

2) Multiply. Give your answer in radical form. (-5-5i)(3-6i)

3) Multiply. Give your answer in radical form. √3√5√17

4) Multiply. Give your answer in radical form. √3(√24+√30)

Answer 1

4)
`6√(2) + 3√(10)`

3)
`√(255)`

2)
`15i - 45`

1)
`16√(3)`

Explanation:

4)
`√(3)[√(24) + √(30)] = √(72) + √(90) = √([2][36]) + √([10][9]) = 6√(2) + 3√(10)`

3)
`√(255) = [√(3)][√(5)][√(17)]`

2)
`[-5 - 5i][3 - 6i] = -15 + 15i + 30{i}^(2) = -15 + 15i - 30 = 15i - 45`

1)
`-4i√(-48) = -4i√([3][16][i]) = -4i[4i]√(3) = -16{i}^(2) √(3) = 16√(3)`

Extended Information on the Complex Number System

`√(-1) = i`

`-1 = {i}^(2)`

`-i = {i}^(3)`

`1 = {i}^(4)`

I am joyous to assist you anytime.

Answer 2

1. 16√3
2. -45+15i
3. √255
4. 6√2 +3√10

Explanation:

1)

`-4i√(-48)=-4i√((-1)(4^2)(3))=(-4i)(4i)√(3)=16√(3)`

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2)

`(-5-5i)(3-6i)=-5(3-6i)-5i(3-6i)=-15+30i-15i+30i^2=-15-30+15i\\\\=-45+15i`

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3)

`√(3)√(5)√(17)=√(3\cdot 5\cdot 17)=√(255)`

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4)

`√(3)(√(24)+√(30))=√(3\cdot 24)+√(3\cdot 30)=√(6^2\cdot 2)+√(3^2\cdot 10)\\\\=6√(2)+3√(10)`

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The applicable identities are ...

`√(a^2b)=a√(b)\\\\i^2=-1`