## c0rtez 3 years ago Two opposite vertices of a square are given by the complex numbers z1=-3+7i and z2=9-9i. Find the other two vertices of the square and give also the equation of its circumscribed circle. Any tips are appreciated.

1. c0rtez

I was thinking to find the mid point between the two vertices and then find the other two vertices using that mid point and different directions. I already found the mid point (3-i).

2. shivam_bhalla

@c0rtez |dw:1337534609410:dw| Do you know rotation ?? i.e $\large z_4 - z_1 = \frac{z_2-z_1}{|z_2-z_1|} * |z_4-z_1|$ Since |z_4-z_1| = |z_2-z_1| (side of square are equal ) Now you will get z_4. Similarly find z_3

3. shivam_bhalla

oops . Sorry It should be $\large z_4 - z_1 = \frac{z_2-z_1}{|z_2-z_1|} * |z_4-z_1| * e^{i (\-pi /2)}$

4. shivam_bhalla

Typo: e^(i * pi/2)

5. c0rtez

Ok thanks I will try to solve it now.

6. shivam_bhalla

Sorry typo again : e^(i * -pi/2)

7. c0rtez

So if I got it right, I can multiply z1 by e^(i * pi/2) to get z2, and use -pi/2 for z4?

8. shivam_bhalla

@c0rtez, It should be $\large z_4 - z_1 = \frac{z_2-z_1}{|z_2-z_1|} * |z_4-z_1| * e^{-i \pi /2}$ Since |z_4-z_1| = |z_2-z_1| (side of square are equal ) Now you will get z_4 from above Use the same technique and find z_3