Simplify

-5 (1+2i) (4+ square root of -1)

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You have `-5(1+2i)(4 + sqrt(-1))` ;

Recall that `sqrt(-1) = i`

So it rewritting it: `-5(1+2i)(4+i)`

Then apply distributive property of multiplication. Do first -5(1+2i).

`(-5 - 10i) (4 + i)`

`-5*4 + (-5*i) + -10i*4 + (-10i*i)`

Simplify by combining similar terms. Recall also that i * i = -1.

`-20 - 5i - 40i -10i^2`

`-20-45i -(10*-1)`

`-20 - 45i +10`

Therefore, the answer is -10 - 45i.

``

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

it gives two different equations: First:

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

Second:

`-5(1+2i)(4-i)=-5(4+8i-i+2)=-5(6+7i) `

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