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[Aruarian Reflection]

I'm trying to solve the following equation:

e^(2z) + e^(z) + 1 = 0, where z is the standard complex number x+iy. I need to solve for z, no idea how to approach this

 

[Macam]

I'm rusty, but I believe it'd be a simple matter of taking the natural log (ln) of the left side to eliminate the e's (yielding, 2z + z + 0) and then solving for z from there. The only stipulation is that ln(0) doesn't exist for the right side to keep the equation equal, so there's likely an algebraic workaround or property to tackle that. Hope that helps as a starting point.

 

[Ecrofirt]

I was thinknig of doing pretty much the same thing, but I can't figure how to get it to work.

Maybe you can do something with taking the derivative of both sides? Bah, I'm really rusty with stuff like this

 

[Macam]

I was thinknig of doing pretty much the same thing, but I can't figure how to get it to work.

Maybe you can do something with taking the derivative of both sides? Bah, I'm really rusty with stuff like this

The derviative wouldn't do any good since the derivative of the left side would be near identical: 2e^(2z) + e^(z) = 0. What course is this for SnowWolf? If you give me some idea of the type of course, it'll probably yield a better idea as to how you're supposed to solve it; even better if you can tell us what you're studying at the moment specifically It's not a particularly hard problem since they're just asking you to solve for z and not the x and/or y, which you could only really extrapolate domains out of anyway.