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c0rtez
Group Title
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
 2 years ago
c0rtez Group Title
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
 2 years ago

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c0rtez Group TitleBest 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).
 2 years ago

shivam_bhalla Group TitleBest 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
 2 years ago

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

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

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

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

c0rtez Group TitleBest 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?
 2 years ago

shivam_bhalla Group TitleBest 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
 2 years ago
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