Can We Solve A Non-Standard Equation? | Problem

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This channel is dedicated to the fascinating realm of Complex Numbers. I trust you'll find the content I'm about to share quite enjoyable. My initial plan is to kick things off with informative lectures on Complex Numbers, followed by a diverse range of problem-solving videos.
❤️ This is Problem #135 on this channel!!! ❤️
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[@charlesokuom8747]

Well explained

[@aplusbi]

Thank you!

[@scottleung9587]

Yay, I got it! (BTW I think this is Problem #135.)

[@aplusbi]

Yay!
Thanks. Changes made

[@leif1075]

​@@aplusbiBut LAMBERT IS A CHEAT ITS CONTRIVED you either know it or you don't so why don't you Please solve in a REAL.WAY WITHOUT LAMBERT PLEASE.

[@JourneyThroughMath]

Lamber W! Lambert W!

[@JourneyThroughMath]

I want the record to show I predicted lambert w before I watched.

[@aplusbi]

You are a legend!

[@soumyadeepbasu6903]

Taylor expansion of ln(1+x) 🌝😅

[@moeberry8226]

Understand that’s only true for W(1) it’s not always the case that e^-x=x

[@aplusbi]

Yessir! 😁

[@JefiKnight]

Interesting there are no complex solutions. It seems like there could be.

[@Skyler827]

W is multivalued, it has infinitely many branches that return complex numbers for every complex input. W_0 and W_-1 are the branches that produce real numbers for real input values.

[@JefiKnight]

Yes, and if I understand correctly, W(1) uses only branch 0 so there is only that one real solution.

[@oenrn]

ln z = -z
e^ln z = e^-z
z = 1/(e^z)
z e^z = 1
W(z e^z) = W(1)
z = W(1)

[@Nobodyman181]

L W func