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What is the modulus (absolute value) of ?Don't round. If necessary, express your answer as a radical.
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Q. What is the modulus (absolute value) of ?Don't round. If necessary, express your answer as a radical.
- Calculate modulus of complex number: The modulus (absolute value) of a complex number is given by the square root of the sum of the squares of its real part () and its imaginary part (). So, for the complex number , we need to calculate the square root of .
- Square the real part: First, we square the real part, which is . So, equals .
- Square the imaginary part: Next, we square the imaginary part, which is . So, equals .
- Add squares of real and imaginary parts: Now, we add the squares of the real and imaginary parts together. This gives us , which equals .
- Take square root of the sum: Finally, we take the square root of to find the modulus of . Since is not a perfect square, we leave it under the radical as .
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