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Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −81\sqrt{-81}

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Full solution

Q. Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −81\sqrt{-81}
  1. Splitting Square Roots: Express −81\sqrt{-81} as the product of square roots and −1\sqrt{-1}.\newline−81=−1×81\sqrt{-81} = \sqrt{-1 \times 81}
  2. Substitute Values: Express −1\sqrt{-1} as ii and 81\sqrt{81} as 99.\newline−81=−1×81=i×9\sqrt{-81} = \sqrt{-1} \times \sqrt{81} = i \times 9
  3. Combine to Get Complex Number: Combine ii and 99 to get the final complex number.\newline−81=i×9=9i\sqrt{-81} = i \times 9 = 9i

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