maths help

Question

the vertices of a square are z1,z2,z3,z4 taken in anticlockwise order then z3 equals

1. iz1+(1+i)z2

2.iz1+(1-i)z2

3.z1+(1+i)z2

4.(i+1)z1+z2

 

Answer 1

In complex numbers, you can find the vertices of a square using 90 degree rotations from the first point.

So if your first point is a+bi, your next point is -b+ai, next is -a-bi, and finally b-ai.

 

In case you forgot, a 90 degree rotation is (x,y) ---> (-y,x).

None of your answers seem to work. I'll go through one of them.

 

i(a+bi) + (1+i)(-b+ai) = ai -b + -b + ai - bi - a = 2ai-2b - bi - a = (a-2b) + (2a-b)i ......not what you're looking for.

Hope this helps in some way.