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Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −65\sqrt{-65}

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Full solution

Q. Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −65\sqrt{-65}
  1. Split and Simplify: Express −65\sqrt{-65} as the product of square roots and −1\sqrt{-1}.\newline−65=−1×65\sqrt{-65} = \sqrt{-1 \times 65}
  2. Express as Complex Number: Express −1×65\sqrt{-1 \times 65} as a complex number using ii.\newline−65=−1×65\sqrt{-65} = \sqrt{-1} \times \sqrt{65}
  3. Replace with ii: Replace −1\sqrt{-1} with ii.\newline−65=i⋅65\sqrt{-65} = i \cdot \sqrt{65}
  4. Simplify Square Root: Simplify 65\sqrt{65}.\newline65=5×13\sqrt{65} = \sqrt{5 \times 13}
  5. Final Expression: Since 5\sqrt{5} and 13\sqrt{13} cannot be simplified further, the expression remains as i65i \sqrt{65}.

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