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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.
 one year ago
 one year 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.
 one year ago
 one year ago

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c0rtezBest ResponseYou've already chosen the best response.0
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 (3i).
 one year ago

shivam_bhallaBest 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
 one year ago

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

shivam_bhallaBest ResponseYou've already chosen the best response.2
Typo: e^(i * pi/2)
 one year ago

c0rtezBest ResponseYou've already chosen the best response.0
Ok thanks I will try to solve it now.
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.2
Sorry typo again : e^(i * pi/2)
 one year ago

c0rtezBest ResponseYou've already chosen the best response.0
So if I got it right, I can multiply z1 by e^(i * pi/2) to get z2, and use pi/2 for z4?
 one year ago

shivam_bhallaBest 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
 one year ago
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