Vector Question (1 Viewer)

[Nooblet94]

Patel Ex 4K Q11
"The points P and Q are represented by the complex numbers z=1-3i and w=-3+4i respectively. Find a point R on the real axis such that PRQ is a right angled triangle"

This is the only question I've struggled with in this exercise, so I must just be missing something really simple. Anyone care to give me a hand?

 

[math man]

R has coordinates (x,0) as it lies on the real axis, and since we want PRQ to be a right angle triangle that means angle PRQ is 90 degrees which means we want the gradient of QR x gradient of PR = -1, and this will gives us a quadratic in x which when solved gives us x to be -5 and 3, try this and see if you can get it