Geometrical applications of complex numbers (1 Viewer)

[Examine]

Ok So I do not really understand any part of this. How did you guys get to understand it/interpret it?

For example, how would you answer these questions?

3. If P represents the complex number p=2+3i, find the complex number q, represented by point Q on an Argand diagram so that points O, P and Q are in clockwise order, and:
a) Triangle OPQ is an isosceles right angle with Angle O equaling 90 degrees.
b) Triangle OPQ is an isosceles right angle with Angle P equaling 90 degrees.
c) Triangle OPQ is an isosceles right angle with Angle Q equaling 90 degrees.

 

[bobmcbob365]

For (i) Since, you know that Q is P rotated -90 clockwise, you just multiply P by cis (-pi/2)

 

[Marc26]

I've seen this in the Terry Lee textbook I think..
For most of them, you pick a rotating point and multiply by either cis90 or cis-90
If that doesn't work, multiply by cis(alpha) with alpha being the angle you want to rotate by.
Hint: Rotating doesn't always require you to start from the origin