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Express the radical using the imaginary unit, i. Express your answer in simplified form. +-sqrt(-30)=+-

Express the radical using the imaginary unit, i i .\newlineExpress your answer in simplified form.\newline±−30=± \pm \sqrt{-30}= \pm

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Full solution

Q. Express the radical using the imaginary unit, i i .\newlineExpress your answer in simplified form.\newline±−30=± \pm \sqrt{-30}= \pm
  1. Recognize the involvement of imaginary unit i i : Recognize that the square root of a negative number involves the imaginary unit i i , where i2=−1 i^2 = -1 .
    ±−30 \pm\sqrt{-30} can be expressed as ±−1⋅30 \pm\sqrt{-1 \cdot 30} .
  2. Separate the square root of the product: Separate the square root of the product into the product of square roots. ±−1×30=±−1×30\pm\sqrt{-1 \times 30} = \pm\sqrt{-1} \times \sqrt{30}.
  3. Replace −1\sqrt{-1} with ii: Replace −1\sqrt{-1} with ii to express the square root of −1-1 as an imaginary number.\newline±−1×30=±i×30\pm\sqrt{-1} \times \sqrt{30} = \pm i \times \sqrt{30}.
  4. No further simplification of 30\sqrt{30}: Since there is no further simplification of 30\sqrt{30}, the expression is already in its simplest form.\newlineSo, the final expression is ±i⋅30\pm i \cdot \sqrt{30}.

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