4 ms·

You can try it out in Python directly which natively support complex numbers (just use j instead of i): >>> import math >>> z=1+2j >>> z*complex.conju

by rdtsc 2y ago

You can try it out in Python directly which natively support complex numbers (just use j instead of i): >>> import math >>> z=1+2j >>> z*complex.conjugate(z) (5+0j) >>> math.sqrt((z*complex.conjugate(z)).real) 2.23606797749979 >>> abs(z) 2.23606797749979 As we can see abs(z) does the right thing. Try it with a negative imaginary part too and "nicer" values: >> z = 3-4j >>> math.sqrt((z*complex.conjugate(z)).real) 5.0 >>> abs(z) 5.0

jcgrillo 2y ago
This is what made me fall in love with python. It's over now, but it was nice while it lasted.
- anthk 2y ago
  Look the post on Common Lisp (SBCL interpreter) and you will see python as a toy language, as it has to import math :D
hpcjoe 2y ago
Same in Julia, but no need to "import math", its already built in :D joe@zap:~ $ julia _ _ _ _(_)_ | Documentation: https://docs.julialang.org (_) | (_) (_) | _ _ _| |_ __ _ | Type "?" for help, "]?" for Pkg help. | | | | | | |/ _` | | | | |_| | | | (_| | | Version 1.10.5 (2024-08-27) _/ |\__'_|_|_|\__'_| | |__/ | julia> z=1+2*im 1 + 2im julia> z*conj(z) 5 + 0im julia> sqrt(z*conj(z)) 2.23606797749979 + 0.0im julia> abs(z) 2.23606797749979
- zahlman 2y ago
  it isn't necessary in Python, either. GP is only importing it for square roots, but exponentiation (via the ** operator) by .5 works fine with complex numbers in Python as well. It even handles complex exponents (although you'd have to look up the branch cut semantics etc. in the documentation): >>> (1+1j)**(1+1j) (0.2739572538301211+0.5837007587586147j) Ironically, the `math` library doesn't handle that: >>> math.pow(1+1j, 1+1j) Traceback (most recent call last): File "<stdin>", line 1, in <module> TypeError: must be real number, not complex
  - rdtsc 2y ago
    Definitely. I was mainly trying to avoid using `**` as non-Python users might be more familiar with '^' instead.
  - cbolton 2y ago
    Works in Julia: julia> (1+im)^(1+im) 0.2739572538301211 + 0.5837007587586147im
btdmaster 2y ago
Conjugate is also a method: x=1 x.conjugate() x=1+2j x.conjugate()
mike_ivanov 2y ago
watch this: $ sbcl This is SBCL 2.4.8, an implementation of ANSI Common Lisp. * (setf z #C(1 2)) #C(1 2) * (* z (conjugate z)) 5 * (sqrt (* z (conjugate z))) 2.236068 * (abs z) 2.236068

by rdtsc 2y ago

jcgrillo 2y ago

This is what made me fall in love with python. It's over now, but it was nice while it lasted.

anthk 2y ago
Look the post on Common Lisp (SBCL interpreter) and you will see python as a toy language, as it has to import math :D

hpcjoe 2y ago

Same in Julia, but no need to "import math", its already built in :D joe@zap:~ $ julia _ _ _ _(_)_ | Documentation: https://docs.julialang.org (_) | (_) (_) | _ _ _| |_ __ _ | Type "?" for help, "]?" for Pkg help. | | | | | | |/ _` | | | | |_| | | | (_| | | Version 1.10.5 (2024-08-27) _/ |\__'_|_|_|\__'_| | |__/ | julia> z=1+2*im 1 + 2im julia> z*conj(z) 5 + 0im julia> sqrt(z*conj(z)) 2.23606797749979 + 0.0im julia> abs(z) 2.23606797749979

zahlman 2y ago
it isn't necessary in Python, either. GP is only importing it for square roots, but exponentiation (via the ** operator) by .5 works fine with complex numbers in Python as well. It even handles complex exponents (although you'd have to look up the branch cut semantics etc. in the documentation): >>> (1+1j)**(1+1j) (0.2739572538301211+0.5837007587586147j) Ironically, the `math` library doesn't handle that: >>> math.pow(1+1j, 1+1j) Traceback (most recent call last): File "<stdin>", line 1, in <module> TypeError: must be real number, not complex
- rdtsc 2y ago
  Definitely. I was mainly trying to avoid using `**` as non-Python users might be more familiar with '^' instead.
- cbolton 2y ago
  Works in Julia: julia> (1+im)^(1+im) 0.2739572538301211 + 0.5837007587586147im

btdmaster 2y ago

Conjugate is also a method: x=1 x.conjugate() x=1+2j x.conjugate()

mike_ivanov 2y ago

watch this: $ sbcl This is SBCL 2.4.8, an implementation of ANSI Common Lisp. * (setf z #C(1 2)) #C(1 2) * (* z (conjugate z)) 5 * (sqrt (* z (conjugate z))) 2.236068 * (abs z) 2.236068