Subjects complex numbers

Magnitude Product

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Magnitude Product


1. The problem is to simplify the expression $|i \times \sqrt{3}|$. 2. Recall that $i$ is the imaginary unit with magnitude $|i|=1$. 3. The magnitude of a product is the product of the magnitudes: $|a \times b| = |a| \times |b|$. 4. Calculate $|i| = 1$ and $|\sqrt{3}| = \sqrt{3}$ since $\sqrt{3}$ is a positive real number. 5. Therefore, $|i \times \sqrt{3}| = |i| \times |\sqrt{3}| = 1 \times \sqrt{3} = \sqrt{3}$. 6. The final answer is $\sqrt{3}$, which is approximately 1.732.