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Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −100\sqrt{-100}

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Full solution

Q. Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −100\sqrt{-100}
  1. Identify Negative Inside Square Root: First, let's identify the negative inside the square root which indicates we'll be using the imaginary unit ii.
  2. Express as Product: Now, let's express −100\sqrt{-100} as −1×100\sqrt{-1 \times 100}.
  3. Use Imaginary Unit: Next, we know that −1\sqrt{-1} is the imaginary unit ii, and 100\sqrt{100} is 1010.
  4. Simplify Expression: So, −100\sqrt{-100} becomes −1×100\sqrt{-1} \times \sqrt{100} which is i×10i \times 10.
  5. Final Result: Finally, we simplify i×10i \times 10 to 10i10i.

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