Complex Numbers Help :) (1 Viewer)

[edmundsung]

Vertex A of square ABCD is represented by the complex number 5 + 2i and its centre X is represented by 2 + i. Find, in the form a + bi where a and b are real,the complex numbers representing the other three vertices.

Thanks in advance for any help!

 

[Shadowdude]

Are you sure it's a square?

 

[Drongoski]

Labelling the square ABCD anti-clockwise, the other 3 vertices are:

B: 1 + 4i
C: -1 + 0i
D: 3 - 2i



Hey edmund - haven't you already just completed yr HSC?



One way of doing this:

(correct solution posted earlier)

 

[TheMathStudent]

Label the centre O (2+i) and A(5+2i),

OA=3+i, now remember that a square forms 90 degrees at the centre by the vertices. Therefore all you need to get OB, OC and OD is to repeatedly multiply by i (turn by 90 degrees).
OB=-1+3i
OC=-3-i
OD=1-3i

Now just add all the above to vector O (2+i) to get the vertices, which I will leave upto you.

 

[barbernator]

Are you sure it's a square?

youre good bro. it was really hard question so dont feel bad about not being able to get it

 

[Sy123]

Vertex A of square ABCD is represented by the complex number 5 + 2i and its centre X is represented by 2 + i. Find, in the form a + bi where a and b are real,the complex numbers representing the other three vertices.

Thanks in advance for any help!

EDIT: I made a crucial mistake, the working has been changed

Establish the properties of the square (that we will use)

- Diagonals bisect at right angles
- Diagonals bisect each other and are same length.

Let

A = a
B = b
C = c
D = d

X = x

It must follow that:







First find b from the first equation, since we already know x and a
Then solve 2nd and 3rd to find c and d.

 

[Shadowdude]

youre good bro. it was really hard question so dont feel bad about not being able to get it

just saying i did another question similar to it and it was actually a rectangle

 

[Sy123]

I made a mistake in my solution, I originally put
(I edited my post)
i(a-x) = b

when it should be

i(a-x)=b-x