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Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −−82-\sqrt{-82}

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Full solution

Q. Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −−82-\sqrt{-82}
  1. Express as product: First, let's express −−82-\sqrt{-82} as the product of square roots and −1\sqrt{-1}.\newline−−82=−−1×82-\sqrt{-82} = -\sqrt{-1 \times 82}
  2. Use i to simplify: Now, let's use ii to represent −1\sqrt{-1} and simplify.−−82=−−1×82=−i×82-\sqrt{-82} = -\sqrt{-1} \times \sqrt{82} = -i \times \sqrt{82}
  3. Simplify radical form: Finally, we simplify 82\sqrt{82} to its simplest radical form.\newline−i⋅82=−i⋅82-i \cdot \sqrt{82} = -i \cdot \sqrt{82}; since 8282 is already a prime number, it cannot be simplified further.

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