Respuesta :
Answer:
So, this is just
[tex](2+\sqrt{-25}) \cdot (4 - \sqrt{-100})[/tex]
This is
(2 + 5i)(4 - 10i), which is 58 :)
Using complex numbers, the result of the expression is given by: 58
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The basic complex number expression is given by:
[tex]i^2 = -1[/tex], and thus: [tex]\sqrt{-1} = i[/tex]
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The expression is given by:
[tex](2 + \sqrt{-25})\times (4 - \sqrt{-100})[/tex]
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The complex roots are:
[tex]\sqrt{-25} = \sqrt{-1 \times 25} = \sqrt{25}\sqrt{-1} = 5i[/tex]
[tex]\sqrt{-100} = \sqrt{-1 \times 100} = \sqrt{100}\sqrt{-1} = 10i[/tex]
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Replacing into the expression:
[tex](2 + \sqrt{-25})\times (4 - \sqrt{-100}) = (2 + 5i)(4 - 10i)[/tex]
Applying the distributive property:
[tex](2 + 5i)(4 - 10i) = 8 - 20i + 20i - 50i^2 = 8 - 50(-1) = 8 + 50 = 58[/tex]
The result of the expression is 58.
A similar problem is given at https://brainly.com/question/13201088
