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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 Imaginary Unit : First, recognize that the square root of a negative number involves the imaginary unit , where is defined as the square root of .
- Express as Product: Express as .
- Separate Square Roots: Now, separate the square roots to get .
- Replace with i: Replace with to get .
- Final Simplified Form: Since there's no simplification needed for , the expression is already in its simplest form.
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