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April 27th, 2019, 10:56 AM  #1 
Senior Member Joined: Oct 2016 From: Arizona Posts: 207 Thanks: 37 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems.  Question about complex absolute value
If $z$ is a complex number and $z^21=4zi$ can I go ahead and say $$z^21=4zi$$? I'm using this to prove $z^2 \le 9+\sqrt{85}$. I'm not sure what steps to take other than what I mentioned. PLEASE just give a hint. Do not post a full solution, just please tell me how to proceed. Last edited by ProofOfALifetime; April 27th, 2019 at 11:07 AM. 
April 27th, 2019, 11:34 AM  #2 
Senior Member Joined: Oct 2016 From: Arizona Posts: 207 Thanks: 37 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems. 
Oh.. I was able to get it. Nevermind! Tricky but cool problem!

April 27th, 2019, 12:36 PM  #3 
Senior Member Joined: Dec 2015 From: somewhere Posts: 510 Thanks: 79  
April 27th, 2019, 01:39 PM  #4 
Senior Member Joined: Oct 2016 From: Arizona Posts: 207 Thanks: 37 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems. 
I wanted to avoid using $z=a+bi$ but I don't think it's possible.

April 27th, 2019, 06:50 PM  #5 
Senior Member Joined: Oct 2016 From: Arizona Posts: 207 Thanks: 37 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems. 
This problem is much harder than I thought!

April 28th, 2019, 07:35 AM  #6 
Senior Member Joined: Oct 2016 From: Arizona Posts: 207 Thanks: 37 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems. 
Actually, it was hard because I messed up on a part of it so that problem no longer made sense. I finally solved it!

April 29th, 2019, 02:12 PM  #7 
Senior Member Joined: Oct 2016 From: Arizona Posts: 207 Thanks: 37 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems. 
OMG if anyone wants to do this problem, I encourage it! I finally solved it and my goodness it was like a journey! I don't know about you all, but I found this problem challenging but the solution rewarding! SORRY for spamming the thread! NOTE:If you do solve it, DO NOT post a solution since it is from a math journal and technically isn't supposed to be posted online, but DEFINITELY do not post a the solution! Thanks! You guys rock! Last edited by ProofOfALifetime; April 29th, 2019 at 02:26 PM. 

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