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Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −58\sqrt{-58}

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Full solution

Q. Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −58\sqrt{-58}
  1. Breakdown of −58\sqrt{-58}: First, let's break down −58\sqrt{-58} into −1\sqrt{-1} and 58\sqrt{58}.\newline−58=−1×58=−1×58\sqrt{-58} = \sqrt{-1 \times 58} = \sqrt{-1} \times \sqrt{58}
  2. Use of imaginary unit: Now, we know that −1\sqrt{-1} is the imaginary unit ii. So, −58=i×58\sqrt{-58} = i \times \sqrt{58}
  3. Simplify 58\sqrt{58}: Next, we simplify 58\sqrt{58}. Since 5858 is not a perfect square, we leave it under the radical.\newlineSo, −58=i⋅58\sqrt{-58} = i \cdot \sqrt{58}
  4. Write as complex number: Finally, we write the expression as a complex number. The complex number is 0+i×580 + i \times \sqrt{58} or simply i×58i \times \sqrt{58}.

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