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Andrew Read

Arg of roots of a complex number?

Andrew Read
Posted 7 months ago
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Consider

SolveValues[z^3 == (1 - I) Sqrt[2], z] // AbsArg

{{2^(1/3), -(\[Pi]/12)}, {2^(1/3), 
  Arg[-(-1)^(1/3) (1 - I)^(1/3)]}, {2^(1/3), 
  Arg[(-1)^(2/3) (1 - I)^(1/3)]}}

The first root is presented in the expected polar form of a complex number. But Arg has trouble with the other two roots because SolveValues (Solve is the same) doesn't seem to complete the solution (leaving ^(1/3)) behind.

This should be easy. Any suggestions to obtain the expected roots of complex numbers?
POSTED BY: Andrew Read
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With version 12.3 I get satisfactory results with this:

SolveValues[z^3 == (1 - I) Sqrt[2], z] // FullSimplify // 
  AbsArg // FullSimplify
POSTED BY: Gianluca Gorni
Andrew Read
Andrew Read
Posted 7 months ago

Yes that works, thank you.
POSTED BY: Andrew Read 
FullSimplify[
 AbsArg[ComplexExpand@SolveValues[z^3 == (1 - I) Sqrt[2], z]]]

Also works.
POSTED BY: Shenghui Yang
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