Complex numbers from two arrays with Real and Imaginary parts

I have two arrays, containing the real and imaginary parts of a list of complex numbers.

Re = {{Re_number1},{Re_number2},…}
Im = {Im_number1},{Im_number2},…}

I was wondering which is the smartest way to combine these two parts in a single array, containing complex numbers whose real and imaginary parts are taken from the two arrays Re and Im:

Complex = {{Re_number1 + i*Im_number1},…}

I guess there will be different ways to do that, maybe one thing to keep into account is that I will then need to make operations on these new complex numbers that I will create.

EDIT:

As @Belisarius suggested, I have tried with:

field [fullREAL_, fullIMAGINARY_] :=
Complex @@@ (Transpose@{fullREAL, fullIMAGINARY});
field[fullREAL, fullIMAGINARY] // MatrixForm

But it doesn’t seem to work, although I suspect that’s because I have made a syntax error…Can someone show me where? The arrays where I stored my rel and imaginary parts are created this way:

n = L = 8;
sigma = 3;
mu = 0.0;

leftREAL =
Table[{RandomVariate[
NormalDistribution[mu, Exp[-(2*Pi*k*sigma/L)^2]]]}, {k, n/2}];
rightREAL = Reverse[leftREAL] /. {x_, y_} -> {n – x, y};
fullREAL = Join[ {0.0}, Most[leftREAL], rightREAL] // MatrixForm

leftIMAGINARY =
Table[{RandomVariate[
NormalDistribution[mu, Exp[-(2*Pi*k*sigma/L)^2]]]}, {k, n/2 – 1}];
rightIMAGINARY = -Reverse[leftIMAGINARY] /. {x_, y_} -> {n – x, y};
fullIMAGINARY =
Join[ {0.0}, leftIMAGINARY, {0.0}, rightIMAGINARY] // MatrixForm

=================

2

 

Complex @@@ (Transpose@{re, im})
– Dr. belisarius
Apr 13 ’15 at 12:01

1

 

Welcome to Mathematica.SE! I suggest the following: 0) Browse the common pitfalls question 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Read the faq! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign!
– Dr. belisarius
Apr 13 ’15 at 12:02

  

 

Thanks @belisarius, I have edited my question, as I have tried to follow your instructions…but still I cannot make it!
– johnhenry
Apr 13 ’15 at 12:17

  

 

I assume you have numeric values for sigma, L and mu. Remove the curly braces in the first arguments of Table and drop the postfix //MatrixForm. belisarius’ solution require you to have re={0,re1,re2,re3…} while you have re=MatrixForm[{0,{re1},{re2},…,{ren}}]. Similar consideration apply to imaginary parts.
– LLlAMnYP
Apr 13 ’15 at 12:22

1

 

You’ve got undefined symbols n, mu, etc. Then you probably need to ditch the MatrixForm. Pretty much you never use it in an assignment. It’s for display purposes only.
– Michael E2
Apr 13 ’15 at 12:22

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2 Answers
2

=================

Here’s working code with corrected syntax

n = L = 8;
sigma = 3;
mu = 0.0;

leftREAL =
Table[RandomVariate[
NormalDistribution[mu, Exp[-(2*Pi*k*sigma/L)^2]]], {k, n/2}];
rightREAL = Reverse[leftREAL] /. {x_, y_} -> {n – x, y};
fullREAL = Join[{0.0}, Most[leftREAL], rightREAL]

leftIMAGINARY =
Table[RandomVariate[
NormalDistribution[mu, Exp[-(2*Pi*k*sigma/L)^2]]], {k, n/2 – 1}];
rightIMAGINARY = -Reverse[leftIMAGINARY] /. {x_, y_} -> {n – x, y};
fullIMAGINARY = Join[{0.0}, leftIMAGINARY, {0.0}, rightIMAGINARY]

Complex @@@ (Transpose@{fullREAL, fullIMAGINARY})

(*{0., -0.00212203, -4.79203*10^-10, 3.36556*10^-22, -1.88384*10^-40,
3.36556*10^-22, -4.79203*10^-10, -0.00212203}*)

(*{0., 0.00201095, 3.07046*10^-10, -9.41259*10^-23, 0.,
9.41259*10^-23, -3.07046*10^-10, -0.00201095}*)

(*{0. + 0. I, -0.00212203 + 0.00201095 I, -4.79203*10^-10 +
3.07046*10^-10 I, 3.36556*10^-22 – 9.41259*10^-23 I, -1.88384*10^-40 + 0. I, 3.36556*10^-22 + 9.41259*10^-23 I, -4.79203*10^-10 – 3.07046*10^-10 I, -0.00212203 – 0.00201095 I}*)

Perhaps I’m missing something, but why not do

Most[leftREAL] + I leftIMAGINARY
rightREAL + I rightIMAGINARY

These could then be put into a single array if desired.

Alternatively

Flatten[fullREAL + I fullIMAGINARY] // MatrixForm

Note that I have preemptively removed MatrixForm from the “full…” assignments and only applied it at the end as it sometimes discombobulates functions along the way.