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Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −84\sqrt{-84}

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Full solution

Q. Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −84\sqrt{-84}
  1. Use Imaginary Unit: Now, we know that −1\sqrt{-1} is the imaginary unit ii. So, −84\sqrt{-84} becomes i×84i \times \sqrt{84}.
  2. Factor and Simplify: Next, we simplify 84\sqrt{84}. The number 8484 can be factored into 4×214 \times 21, and 44 is a perfect square.\newline84=4×21=4×21=2×21\sqrt{84} = \sqrt{4 \times 21} = \sqrt{4} \times \sqrt{21} = 2 \times \sqrt{21}
  3. Combine Imaginary Unit: Now we can combine the imaginary unit with the simplified radical. i⋅84=i⋅2⋅21i \cdot \sqrt{84} = i \cdot 2 \cdot \sqrt{21}
  4. Multiply to Get Complex Number: Finally, we multiply the ii by 22 to get the complex number.i×2×21=2i×21i \times 2 \times \sqrt{21} = 2i \times \sqrt{21}

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