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Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −31\sqrt{-31}

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Full solution

Q. Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −31\sqrt{-31}
  1. Recognize Negative Square Root: First, recognize that −31\sqrt{-31} involves the square root of a negative number, which can be expressed using the imaginary unit ii.\newline−31=−1×31\sqrt{-31} = \sqrt{-1 \times 31}
  2. Separate Terms: Next, separate the square root of −1-1 from the square root of 3131.−1×31=−1×31\sqrt{-1 \times 31} = \sqrt{-1} \times \sqrt{31}
  3. Replace with Imaginary Unit: Replace −1\sqrt{-1} with ii to express the square root of −1-1 as an imaginary number.\newline−1×31=i×31\sqrt{-1} \times \sqrt{31} = i \times \sqrt{31}
  4. Simplify as Complex Number: Now, simplify the expression by writing it as a complex number. i31=i31i \sqrt{31} = i \sqrt{31}

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