Question

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

Answer 1

Set up a imaginary coordinate plane and plot the point, the absolute value, or the modulus is the length of the line from (0,0)

Explanation:

An imaginary plane is just like your regular `x,y` plane but instead of `y` in the vertical axis we have `i`, starting from `1i,2i, 3i, 4i...`, the x axis remains the same. The point `5-12i` 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 `4th` 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 + (-12)^2) = sqrt(169)`