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DanielAcedo

  • 3 years ago

How do I simplify the expression 4+√-4+i i being an imaginary number.

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  1. LogicalApple
    • 3 years ago
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    Is that \[4 + \sqrt{-4} + i\] or \[4 + \sqrt{-4 + i}\]

  2. DanielAcedo
    • 3 years ago
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    The first one

  3. LogicalApple
    • 3 years ago
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    Oh ok, thank you. Would you agree that \[\sqrt{-4} = \sqrt{(-1)(4)} = \sqrt{-1} * \sqrt{4}\]

  4. DanielAcedo
    • 3 years ago
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    Yes

  5. LogicalApple
    • 3 years ago
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    And \[\sqrt{-1} = i\]

  6. DanielAcedo
    • 3 years ago
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    Yes, isnt also i^2 -1

  7. LogicalApple
    • 3 years ago
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    That is true as well

  8. LogicalApple
    • 3 years ago
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    So we see how \[\sqrt{-4} = \sqrt{-1} * \sqrt{4} = i * 2 = 2i\]

  9. DanielAcedo
    • 3 years ago
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    Ohh I see

  10. DanielAcedo
    • 3 years ago
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    So would my answer be 4+3i ?

  11. LogicalApple
    • 3 years ago
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    Yes, that is right

  12. DanielAcedo
    • 3 years ago
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    Oh Ok, Thank you!

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