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It turns out that the HP Prime does have rectangular-polar conversion functions. They are buried in the catalog.

Syntax:

rectangular_coordinates(r, θ) or rectangular_coordinates([r, θ]) returns the vector [x, y]

Example: (Radians mode - CAS mode, works in Home mode too)
rectangular_coordinates(3, π/3) returns [3/2, 3*√(3)/2] (≈ [1.5, 2.59807621135] )

polar_coordinates(x,y) or polar_coordinates([x,y]) returns the vector [r, θ]

Example:
polar_coordinates(3,4) returns [5, ATAN(4/3)] (≈ [5, .927295218002] )
Hi Eddie,

Even much more easy, with version 5447 (2013 11 25),

Enter your rectangular like
7+9*i
then press [SHIFT] then [x] //where the angle symbol <) is, and will show

11.40...<)52.12... // in degrees

or

11.40...<).90... // in radians

It help me much and I hope to You too.
best regards!!
joseph
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