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Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −14\sqrt{-14}

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Full solution

Q. Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −14\sqrt{-14}
  1. Split and Simplify: Express −14\sqrt{-14} as the product of square roots and −1\sqrt{-1}.−14=−1×14\sqrt{-14} = \sqrt{-1 \times 14}
  2. Express as Complex Number: Express −1×14\sqrt{-1 \times 14} as a complex number using ii.\newline−14=−1×14\sqrt{-14} = \sqrt{-1} \times \sqrt{14}
  3. Replace and Simplify: Replace −1\sqrt{-1} with ii and simplify 14\sqrt{14}.\newline−14=i×14\sqrt{-14} = i \times \sqrt{14}
  4. Simplify Radical Form: Simplify 14\sqrt{14} to its simplest radical form.14\sqrt{14} is already in its simplest radical form.
  5. Combine for Final Result: Combine ii and 14\sqrt{14} to express the final complex number.\newline−14=i14\sqrt{-14} = i \sqrt{14}

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