A complex numbers question: 3+2i is the center of a square, and one vertex is -1+5i. Find the others.

Question

terenzreignz · Answer

What's the difference? (between 3+2i and -1+5i)

anonymous · Answer

|dw:1382534238040:dw|

terenzreignz · Answer

The only way I know how to do this is by using intuition.
Now, what's 3+2i - (-1+5i) ?

terenzreignz · Answer

huh... this is annoying.. sorry, must rethink...

anonymous · Answer

yes yes

terenzreignz · Answer

Maybe it's easier to imagine these as if they were vectors? After all, I can hardly see how the fact that $$\large i^2 = -1$$ factors into any of this...

anonymous · Answer

ok so tell me: what graphical translation happens when you multiply the whole thing by i, -i and -1??

terenzreignz · Answer

Oh yeah, that, hang on, intuition happening XD

terenzreignz · Answer

Okay, imagine our z-3-2i instead.

terenzreignz · Answer

so that our center happens to be 0.

anonymous · Answer

wait hold on

anonymous · Answer

ok so i just checked my notes, and i think that multiplying by i is a 90 degrees clockwise rotation

anonymous · Answer

so by -i is a 90 degrees anticlockwise rotation.

terenzreignz · Answer

Yup.

anonymous · Answer

so bascially if the center is C, and the vertex is V1, then i do V1 - C to get CV1