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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.
- Replace with imaginary unit: Now, we know that is the imaginary unit , so we can replace that part of the expression.
- Simplify square root of : Next, we simplify by finding the prime factors of and looking for pairs to take out of the square root.We can take a pair of out of the square root as .
- Combine and square root: Now we can combine the and the simplified square root to get the final complex number.
- Write final complex number: Finally, we write the expression as a complex number.But wait, we made a mistake here. We should have written as .
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