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Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −43\sqrt{-43}

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Full solution

Q. Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −43\sqrt{-43}
  1. Express as product: Express −43\sqrt{-43} as the product of square roots and −1\sqrt{-1}.−43=−1×43\sqrt{-43} = \sqrt{-1 \times 43}
  2. Replace with i: Replace −1\sqrt{-1} with ii to get the complex number.\newline−43=−1×43=i×43\sqrt{-43} = \sqrt{-1} \times \sqrt{43} = i \times \sqrt{43}
  3. Simplify radical: Simplify the radical 43\sqrt{43} if possible.\newlineSince 4343 is a prime number, it cannot be simplified further.\newlineSo, the expression remains i43i \sqrt{43}.

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