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Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −51\sqrt{-51}

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Full solution

Q. Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −51\sqrt{-51}
  1. Breakdown of −51\sqrt{-51}: First, let's break down −51\sqrt{-51} into −1\sqrt{-1} and 51\sqrt{51}.\newline−51=−1×51\sqrt{-51} = \sqrt{-1 \times 51}
  2. Use of imaginary unit: Now, we know that −1\sqrt{-1} is the imaginary unit ii. So, −51=i×51\sqrt{-51} = i \times \sqrt{51}
  3. Final expression: We can't simplify 51\sqrt{51} any further since 5151 is not a perfect square.\newlineSo the expression stays as i⋅51i \cdot \sqrt{51}.

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