Questions: Multiply. [ (sqrt-9)(sqrt-49) ] [ (sqrt-9)(sqrt-49)= ] (Simplify your answer.)

Multiply.
[
(sqrt-9)(sqrt-49)
]
[
(sqrt-9)(sqrt-49)=
]
(Simplify your answer.)
Transcript text: Multiply. \[ (\sqrt{-9})(\sqrt{-49}) \] \[ (\sqrt{-9})(\sqrt{-49})= \] $\square$ (Simplify your answer.)
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Solution

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Solution Steps

Step 1: Recognize the multiplication of two complex numbers

Given two complex numbers in the form of ab\sqrt{-a} \cdot \sqrt{-b}, where aa and bb are non-negative real numbers.

Step 2: Convert to imaginary form using a=ia\sqrt{-a} = i\sqrt{a} and b=ib\sqrt{-b} = i\sqrt{b}

This gives us iaibi\sqrt{a} \cdot i\sqrt{b}.

Step 3: Multiply the expressions

Multiplying the expressions gives us i2abi^2\sqrt{ab}.

Step 4: Simplify using i2=1i^2 = -1

This simplifies to ab-\sqrt{ab}.

Final Answer

The result of multiplying 9\sqrt{-9} and 49\sqrt{-49} is 441-\sqrt{441} = -21.

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