Mastering Complex Numbers in Mathematica: A Comprehensive Tutorial

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Discussion Overview

The discussion revolves around using Mathematica for operations involving complex numbers, particularly in solving equations that include complex variables. Participants share their experiences, challenges, and solutions related to manipulating complex numbers within the software.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant expresses a need for tutorials on handling complex numbers in Mathematica, especially for solving complex equations.
  • Another participant suggests using the Solve function for a specific set of complex equations, indicating it can be treated like normal equations.
  • A participant asserts that there is nothing particularly special about using complex numbers in Mathematica.
  • It is mentioned that for linear equations, one can convert them to matrix form and use row reduction.
  • A participant seeks help with conjugating expressions involving exponentials and converting them to trigonometric form.
  • Another participant recommends using the ExpToTrig function to convert exponential expressions to trigonometric functions.
  • A participant points out the existence of a Conjugate function for obtaining the conjugate of complex numbers.
  • One participant notes that the Mathematica help resources are useful for finding functions related to specific tasks.
  • A participant shares their success in using the suggested functions to solve their problem, expressing gratitude for the assistance received.

Areas of Agreement / Disagreement

Participants generally agree on the utility of Mathematica for handling complex numbers, though there are varying levels of comfort and familiarity with specific functions. Some participants express challenges, while others provide solutions, indicating a mix of experiences and knowledge.

Contextual Notes

Some participants mention specific functions and methods without detailing their limitations or assumptions, such as the conditions under which certain functions are applicable or the nature of the equations being solved.

liskawc
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so i was kind of wondering if anyone knows of any mathematica tuorials for how to operate with complex numbers (i know how to do it by hand but solving a set of 5 equations all complex just seems suicidal :D )

so any help d be appreciated
 
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What about

Solve[{
a^2 + b^2 == -2,
b - 3 c == \[ImaginaryI],
2 c - 3 a == 1 + \[ImaginaryI],
d + 4 == Sqrt[e],
e + a == -3},
{a, b, c, d, e}
]

just as you would solve a normal set of equations?
 
There's really nothing special at all about using complex numbers in Mathematica.

- Warren
 
By the way, if the equations are linear, there is nothing suicidal about it. Just write them in matrix form and row-reduce :smile: (the joy of every student)

Oh, and before I forget, you make the imaginary i in Mathematica by typing I (capital i) or [Escape]ii[Escape]
 
Last edited:
hmm yeah i wish they were linear

well only problem i really got is that i don't know how to conjugate Exp[ i x] or to make shown as Cosx + i Sinx

P.S equations were:
a1 - a2 + b1 - b2

-(20/197) Sqrt[2555] (a2 - b2) Sqrt[-1 + x] +
20/197 Sqrt[2555] (a1 - b1) Sqrt[x]

-a3 exp[20/197 \[ImaginaryI] Sqrt[2555] Sqrt[-2 + x]] +
b2 exp[-(20/197) \[ImaginaryI] Sqrt[2555] Sqrt[-1 + x]] +
a2 exp[20/197 \[ImaginaryI] Sqrt[2555] Sqrt[-1 + x]]

-(20/197) Sqrt[2555] a3 Sqrt[-2 + x]
exp[20/197 \[ImaginaryI] Sqrt[2555] Sqrt[-2 + x]] +
20/197 Sqrt[2555]
Sqrt[-1 +
x] (a2 exp[20/197 \[ImaginaryI] Sqrt[2555] Sqrt[-1 + x]] -
b2 exp[20/197 \[ImaginaryI] Sqrt[2555] Sqrt[-1 + x]])

(dunno latex so sry for the uglyness)
 
Last edited:
you can use ExpToTrig[...] to convert the exponentials to trigonometric functions.

I think there is a conjugation function somewhere...
 
You'd never guess it... it's called Conjugate[...]
i.e. Conjugate[4 + 3I] gives 4 - 3I
 
The mathematica help is pretty good, just do a search in the mathematica help browser for whatever you're trying to do, there is probably a function already designed for it.
 
i think i actually managed it :D did the trig thingy and then used Conjugate (that one was silly obvious /blush)
and i got a result

thank you :)
 

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