Mathematica Mastering Complex Numbers in Mathematica: A Comprehensive Tutorial

AI Thread Summary
The discussion centers around the use of Mathematica for solving equations involving complex numbers. Users express the need for tutorials on handling complex numbers in Mathematica, particularly when faced with a set of five complex equations. It is noted that solving such equations is straightforward in Mathematica, similar to linear equations, and can be approached using matrix forms and row-reduction techniques. The conversation highlights specific functions in Mathematica, such as using "I" for the imaginary unit and the "ExpToTrig" function to convert exponential forms to trigonometric forms. Users also mention the "Conjugate" function for obtaining the conjugate of complex numbers. Overall, the thread emphasizes the accessibility of Mathematica's capabilities for complex number operations and encourages users to utilize the built-in help resources for guidance.
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]
 
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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)
 
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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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