College Algebra: Absolute value of a complex number in Argand's diagram

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We can define absolute value as

$d_{(x,y)}=|x-y|$

where the distance from $x$ to $y$ is the absolute value of $x-y$.

For example

$|4-2| = 2$ because two is the distance from four to two in the number line.

$|-2-1| = 3$ because three is the distance from negative two to one in the number line.

A complex number can be expressed in this way:

$z=a+bi$

Then

$|z|=a+bi$

is equivalent to

$d_{(a,-bi)}=|a-(-bi)|$

We can use Argand's diagram to form a triangle that has a side $a$, and another side $-bi$.

Then

$|z|=\sqrt{a^2+(-bi)^2}$

$|z|=\sqrt{a^2+b^2}$

Although the result is correct, I am not sure if keeping this way of thinking will set me up for future mistakes, as the $-bi$ part goes into the "negative imaginaries." Please let me know, and I apologize for my lax explanation and terminology. I am getting into math and I would appreciate your support.