复数模

Given a complex number $z = a + bi$, its magnitude is $|z| = \sqrt{a^2+b^2}$

We denote magnitude as |z|, just like absolute value.

Reasoning: If z is a real number, then the magnitude of z is just its absolute value.

Let's say $z =$ r cis $\theta$ (polar form)

Then obviously $|z| = r$

Some useful identities with magnitude (when it's not 0) are the following: $|ab| = |a||b|, |\frac{a}{b}|=\frac{|a|}{|b|}$

Furthermore, just like $|x+y| \le |x| + |y|$ for absolute value, we have $|x+y| \le |x|+|y|$ for magnitudes.

It's just $|12+5i|=13$ divided by $|3+4i|=5$ to give 2.6

It may also be helpful to note $|z| = |\overline{z}|$

Also, $z \cdot \overline{z} = |z|^2$

That's the basics of magnitude!