Okay forget modulus.
We wanna find the area of triangle, so we'll take AC as base. To find the distance AC, we can use the distance formula (from coordinate geometry) or simply think about it. The line is vertical, so we just need to find the difference in i components of A and C. You'll get 2*sqrt(2).
For the height part, we just measure the horizontal distance between B and A, which is simply the difference in x coordinates of them, or the difference in real part of the numbers. That gives you 5*sqrt(2). Hope that's clear.
Edit: since you know all the coordinates, you can also use the Shoelace Formula for finding its area.
So for y coordinates is it important to mention iota? Thanks a lot btw, got the rest.
View attachment 60023
Maybe spoiler buttons are getting annoying for some.
Why is cos^2x = 0 if dy/dx is 0 for stationary point?