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Use the imaginary number to rewrite the expression below as a complex number. Simplify all radicals.
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Q. Use the imaginary number to rewrite the expression below as a complex number. Simplify all radicals.
- Recognize Breakdown: First, recognize that can be broken down into .
- Rewrite Imaginary Unit: Next, is the definition of the imaginary unit , so we can rewrite the expression as .
- Calculate Square Root: Now, is a perfect square, which equals . So the expression becomes .
- Final Simplification: Finally, since multiplication is commutative, we can write it as or simply .
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