Complex Numbers Help (1 Viewer)

[Andy005]

Thanks for the help.

 

[darkk_blu]

its an isoceles so you know that the other angles are 45 and 45, you do z1 - z2, then you rotate by 45 degree by multiply cis 45 then divide by root2 bc its shorter side of triangle then add it back to find z3, also do cis-45 and there should be 2 answers for z3

 

[captainhelium]

Eek I haven't done 4U in a while so I might be a bit rusty but this is what I got - hopefully it's right.

https://i.imgur.com/a8xeaNY.jpg

Essentially, since it's an isosceles triangle with z₃ as a right angle, the remaining angles would be 45 degrees. Therefore, I think you can just manipulate the vector z₁ and z₂ by multiplying it with cis(pi/4) or cis (-pi/4) to eventually find z₃.

Hopefully the working out in the image makes sense.

If I'm wrong let me know - I haven't done this in a while so I might've forgot some stuff.

Also, I believe you can have two values of z₃ I think - one above the real axis and one below the real axis. I'm not fully sure though.

 

[darkk_blu]

Eek I haven't done 4U in a while so I might be a bit rusty but this is what I got - hopefully it's right.

https://i.imgur.com/a8xeaNY.jpg

Essentially, since it's an isosceles triangle with z₃ as a right angle, the remaining angles would be 45 degrees. Therefore, I think you can just manipulate the vector z₁ and z₂ by multiplying it with cis(pi/4) or cis (-pi/4) to eventually find z₃.

Hopefully the working out in the image makes sense.

If I'm wrong let me know - I haven't done this in a while so I might've forgot some stuff.

Also, I believe you can have two values of z₃ I think - one above the real axis and one below the real axis. I'm not fully sure though.

Its wrong, but close. Check the moduli of the vectors, they don’t add up correctly, z1 to z2 is 5 but multiplying by Cis/4 only rotates it, it’s new moduli is also 5, which is incorrect, it should be shorter. I have the correct working out but can’t type it up until I get home, I’ll post again if I remember, the answer should be divided by sqrt2

 

[captainhelium]

Its wrong, but close. Check the moduli of the vectors, they don’t add up correctly, z1 to z2 is 5 but multiplying by Cis/4 only rotates it, it’s new moduli is also 5, which is incorrect, it should be shorter. I have the correct working out but can’t type it up until I get home, I’ll post again if I remember, the answer should be divided by sqrt2

Ah yep that's true - silly mistake from me haha haven't done 4U in a while rip xD.

Thanks for clearing that up!