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Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −−33-\sqrt{-33}

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Full solution

Q. Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −−33-\sqrt{-33}
  1. Break into parts: First, let's break −−33-\sqrt{-33} into −1-1 times −33\sqrt{-33}.\newline−−33=−1×−33-\sqrt{-33} = -1 \times \sqrt{-33}
  2. Use imaginary unit: Now, we know that −1\sqrt{-1} is the imaginary unit ii. So we can write −33\sqrt{-33} as −1×33\sqrt{-1\times33}.\newline−1×−33=−1×−1×33-1 \times \sqrt{-33} = -1 \times \sqrt{-1\times33}
  3. Separate and replace: Next, we separate the square roots and replace −1\sqrt{-1} with ii.−1×−1×33=−1×−1×33-1 \times \sqrt{-1\times33} = -1 \times \sqrt{-1} \times \sqrt{33}−1×−1×33=−1×i×33-1 \times \sqrt{-1} \times \sqrt{33} = -1 \times i \times \sqrt{33}
  4. Simplify expression: Finally, we simplify the expression to get the complex number.\newline−1×i×33=−i×33-1 \times i \times \sqrt{33} = -i \times \sqrt{33}

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