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Does the question even make sense? How does abs value interact with imaginary numbers?

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> What is the absolute value of i?

1

> Does the question even make sense?

Yes.

> How does abs value interact with imaginary numbers?

The absolute value of a number is its distance from zero in the complex plane. This is the direct generalization of the notion of absolute value on real numbers, where the absolute value is defined as the distance of a real number from zero on the real number line.

So, by the Pythagorean theorem, the absolute value of a complex number is calculated like this:

|*x* + *y*i| = √\(*x*^(2) + *y*^(2)\)

*[In the above formula, x and y are real numbers, of course.]*
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Think about it as distance from (0,0) in the complex plane. By that I mean a+bi where a and b are 0.
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The absolute value of **a + bi** = ✓(a^2 + b^2 ) for all real *a* and *b*

So the absolute value for **i** is simply 1.

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