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Simplify this equation: `-5(1+2i)(4+sqrt(-1))`

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rosey-girl | Student, Grade 12 | Valedictorian

Posted May 15, 2013 at 9:44 PM via web

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Simplify this equation:

`-5(1+2i)(4+sqrt(-1))`

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violy | High School Teacher | (Level 3) Assistant Educator

Posted May 15, 2013 at 10:23 PM (Answer #1)

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Take note that `sqrt(-1) = i.`

Hence, we will have:

`-5(1 + 2i)(4 + i) `

We use foil method here.

`-5((1*4) + (1*i) + (2i*4) + (2i*i)) = -5(4 + i + 8i + 2i^2)`

Combine like terms. 

`-5(4 + 9i + 2i^2)`

Take note that i^2 = -1.

`-5(4 + 9i + 2(-1)) = -5(4 + 9i - 2) = -5(2 + 9i)`

Apply Distributive Property.

`-5(2 + 9i) = -10 - 45i`

Therefore, the answer is -10 - 45i.

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oldnick | Valedictorian

Posted May 15, 2013 at 10:54 PM (Answer #2)

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`-5(1+2i)(4+i)=-5(4+i+8i+2i^2)=-5(4+9i-2)=-5(2+9i)`

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