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 2 years ago
Two opposite vertices of a square are given by the complex numbers z1=3+7i and z2=99i. Find the other two vertices of the square and give also the equation of its circumscribed circle.
Any tips are appreciated.
 2 years ago
Two opposite vertices of a square are given by the complex numbers z1=3+7i and z2=99i. Find the other two vertices of the square and give also the equation of its circumscribed circle. Any tips are appreciated.

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c0rtez
 2 years ago
Best ResponseYou've already chosen the best response.0I 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 (3i).

shivam_bhalla
 2 years ago
Best ResponseYou've already chosen the best response.2@c0rtez dw:1337534609410:dw Do you know rotation ?? i.e \[\large z_4  z_1 = \frac{z_2z_1}{z_2z_1} * z_4z_1\] Since z_4z_1 = z_2z_1 (side of square are equal ) Now you will get z_4. Similarly find z_3

shivam_bhalla
 2 years ago
Best ResponseYou've already chosen the best response.2oops . Sorry It should be \[\large z_4  z_1 = \frac{z_2z_1}{z_2z_1} * z_4z_1 * e^{i (\pi /2)}\]

shivam_bhalla
 2 years ago
Best ResponseYou've already chosen the best response.2Typo: e^(i * pi/2)

c0rtez
 2 years ago
Best ResponseYou've already chosen the best response.0Ok thanks I will try to solve it now.

shivam_bhalla
 2 years ago
Best ResponseYou've already chosen the best response.2Sorry typo again : e^(i * pi/2)

c0rtez
 2 years ago
Best ResponseYou've already chosen the best response.0So if I got it right, I can multiply z1 by e^(i * pi/2) to get z2, and use pi/2 for z4?

shivam_bhalla
 2 years ago
Best ResponseYou've already chosen the best response.2@c0rtez, It should be \[\large z_4  z_1 = \frac{z_2z_1}{z_2z_1} * z_4z_1 * e^{i \pi /2}\] Since z_4z_1 = z_2z_1 (side of square are equal ) Now you will get z_4 from above Use the same technique and find z_3
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