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Clash Royale CLAN TAG #URR8PPP up vote 7 down vote favorite Let $z$ be a complex number satisfying $$(z+1)^100 = (z-1)^100$$ Show that $z$ is purely imaginary, i.e. that $Re(z) = 0$. Rearrange to $$left(fracz+1z-1right)^100 = 1$$ I tried using $z = x+iy$ and trying to multiply numerator and denominator by the conjugate, but I hit a roadblock. I also tried substituting $1 = -e^ipi$, but that also doesn't seem to get me anywhere. How can I prove this? Any help is appreciated, thank you! complex-analysis complex-numbers share | cite | improve this question edited 3 mins ago TheSimpliFire 11k 6 21 54 asked 7 hours ago Chinmayee Gidwani 46 2 New contributor Chinmayee Gidwani is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct. add a comment  |  up vote 7 down vote favorite Let $z$ be a complex number sa...

Clash Royale CLAN TAG #URR8PPP .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty margin-bottom:0; up vote 0 down vote favorite For the past few years I've been weighing up the decisions on whether to transition from male to female by seeing doctors, therapists and doing research into the procedures/medication I may have to take. I've decided that I want to transition. as I am currently employed I have been wondering when should let my employers know of this change. I know I will have to tell them at some point as my employment records will need to be updated however I don't know if I should let them know prior or wait until I've transitioned. I know that because I live in Australia it would be illegal for my employers to terminate me because of this decision and I have been accumulating sick days and annual leave so I would make sure that my leave is approved before any Surgery, not to mention that where I work has policies against...