# How do you plot 5-12i and find its absolute value?

An imaginary plane is just like your regular $x , y$ plane but instead of $y$ in the vertical axis we have $i$, starting from $1 i , 2 i , 3 i , 4 i \ldots$, the x axis remains the same. The point $5 - 12 i$ would be a point that is a value of $5$ on the horizontal axis and a value of $- 12$ on the vertical axis, so it'll be a point in the $4 t h$ quadrant. You can find the length of this line from 0,0 graphically or algebraically as shown below.
$| z | = \sqrt{{a}^{2} + {b}^{2}}$ where a is the real part and b the imaginary. So the absolute value of the given term is $\sqrt{{5}^{2} + {\left(- 12\right)}^{2}} = \sqrt{169}$