Hey all, Any good resources for simplifying complex numbers?

just use the definition of complex ln
https://en.wikipedia.org/wiki/Complex_logarithm#Definition_of_principal_value

ln(1-i)=ln(|1-i|)+iArg(1-i)=ln(sqrt(2))+i(-pi/4)=ln(2)/2-(pi/4)i

>>8656714
ln is not a function over the complex numbers, just as arctan is not a function over the reals. you're going to have to restrict it to a "branch":
https://en.wikipedia.org/wiki/Complex_logarithm
anyways...
z = ln(1 - i)
e^z = 1 - i
note z = x + iy for x,y real
e^x * e^iy = 1 - i
x = ln(sqrt(2))
y = 7pi/4

>>8656714
What do any of you actually do "of consequence" with all this irrational math? Not including teaching it to a bunch of new kids who, in all likelihood, will also never do anything of consequence with it.

>>8656857
the few of the bunch who actually do something of consequence with it makes it worth it

>>8656857
Same thing could have been said about negative numbers back when only positive integers existed.

Who knows, but a lot of physics (my major) has to do with using imaginary numbers (waves and such). So learning how to deal with them is important.

Also, it's fun.

>>8656857
how awful it is that certain number systems got the name "complex," "imaginary," and "irrational," while others got "rational," "real," and "natural"

>>8656857

> irrational

you mean imaginary

math becomes legitimate the second you generate a fractal with it

>>8656777
>just as arctan is not a function over the reals
What do you mean? Is arctan the one that returns an angle from a slope ratio? How is that not a real number? Or do you mean its range is restricted to 2pi?

>>8656857
I'm a pure math major who took what was basically an applied course of complex numbers (basically calculus on complex numbers, but nothing too rigorous) before complex analysis. That shit was hella fucking applicable for just about anything engineering related.

Also

>irrational math

t. brainlet

>>8656885
look up the definition of a function
you have to restrict the codomain for arctan to be a function