Modify real part and leaves imaginary part unchanged

Question

How can I flip the sign of the real part but not affect the imaginary part of a complex number:

a+bi => -a + bi

Example list:

list = {{-0.282095 + 0.282095 I, -0.27254 + 0.291336 I, 
-0.262018 + 0.300835 I, -0.250437 + 0.310542 I}}

expected:

{{0.282095 + 0.282095 I, 0.27254 + 0.291336 I, 
0.262018 + 0.300835 I, 0.250437 + 0.310542 I}}

So it's "similar" to conjugate but works on the real not imaginary.

WReach · Accepted Answer · 2019-10-01 22:48:56Z

30

-Conjugate[list]

(* {{0.282095 + 0.282095 I, 0.27254 + 0.291336 I, 
     0.262018 + 0.300835 I, 0.250437 + 0.310542 I}} *)

answered Oct 1, 2019 at 22:48

WReach

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$\begingroup$ This is not even a Mathematica but a Math answer. I like it $\endgroup$
– infinitezero
Commented Oct 2, 2019 at 12:06

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Suba Thomas · Accepted Answer · 2019-10-01 22:47:43Z

10

list /. Complex[x_, y_] :> Complex[-x, y]

{{0.282095 + 0.282095 I, 0.27254 + 0.291336 I, 0.262018 + 0.300835 I, 0.250437 + 0.310542 I, 2, 3 I}}

answered Oct 1, 2019 at 22:47

Suba Thomas

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1

$\begingroup$ This assumes that all entries are truly Complex[_,_]. But for a list {{-0.282095 + 0.282095 I, -0.3445}}, which also contains only complex numbers (although one of them happens to be purely real, and even have Real head), this won't work correctly. $\endgroup$
– Ruslan
Commented Oct 3, 2019 at 5:20
$\begingroup$ Agreed. This solution is for complex numbers of the form a + b i that was asked in the question. To include real numbers it needs to be modified to {Complex[x_,y_]:>Complex[-x,y], x_:>-x}. $\endgroup$
– Suba Thomas
Commented Oct 3, 2019 at 14:21
$\begingroup$ Actually this would also break for "complex" number like e.g. 1.234+0I, which actually collapses to a Real $\endgroup$
– Ruslan
Commented Oct 3, 2019 at 14:23

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Michael Seifert · Accepted Answer · 2019-10-02 18:26:00Z

2

f[z_] = -Re[z] + I Im[z]
f[list]

(* {{0.282095 + 0.282095 I, 0.27254 + 0.291336 I, 0.262018 + 0.300835 I, 0.250437 + 0.310542 I}} *)

answered Oct 2, 2019 at 18:26

Michael Seifert

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3 Answers 3