Mastering Complex Numbers in Mathematica: A Comprehensive Tutorial

[liskawc]

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

 

[CompuChip]

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?

 

[chroot]

There's really nothing special at all about using complex numbers in Mathematica.

- Warren

 

[CompuChip]

By the way, if the equations are linear, there is nothing suicidal about it. Just write them in matrix form and row-reduce (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]

 

[liskawc]

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)

 

[NeoDevin]

you can use ExpToTrig[...] to convert the exponentials to trigonometric functions.

I think there is a conjugation function somewhere...

 

[CompuChip]

You'd never guess it... it's called Conjugate[...]
i.e. Conjugate[4 + 3I] gives 4 - 3I

 

[NeoDevin]

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.

 

[liskawc]

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 :)