Thanks Jake! Could you possibly help with this one as well? Its Q. 18 and I've drawn the diagram, but I don't know how to find the diagonal.
Hey! Weird question; you're not usually asked to find the cartesian equation of something on the argand diagram. Still, let's think about what we know.
Firstly, the line must be
perpendicular to the diagonal AC. This is important, because we can find the gradient of the first diagonal, and use that to find the perpendicular gradient. Secondly, the line must
bisect the diagonal AC. Now, we have a gradient and a point; all we need to find the equation!
Let's replace A and C with points on the cartesian plane; A(0, 3) and C(4, -5). The gradient of the line between them will be
So, the gradient of the perpendicular line will be 1/2.
Now, the midpoint of AC is (2, -1). So, the cartesian equation of the line perpendicular to the diagonal AC will be
So, we get the equation
Great! That's the first part down. Now, the second point wants us to show that
Let's let z=x+iy
And we're done!