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Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −62\sqrt{-62}

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Full solution

Q. Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −62\sqrt{-62}
  1. Breakdown of −62\sqrt{-62}: First, let's break down −62\sqrt{-62} into −1\sqrt{-1} and 62\sqrt{62}.\newline−62=−1×62\sqrt{-62} = \sqrt{-1 \times 62}
  2. Use of imaginary unit: Now, we know that −1\sqrt{-1} is the imaginary unit ii. So, −62=i⋅62\sqrt{-62} = i \cdot \sqrt{62}
  3. Simplify 62\sqrt{62}: Finally, we simplify 62\sqrt{62} to its simplest radical form, which is just 62\sqrt{62} since 6262 is not a perfect square.\newlineSo, −62=i⋅62\sqrt{-62} = i \cdot \sqrt{62}

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