How to represent polar coordinates in a easy way?

Question

I've been using the TI-NSpire CX Cas calculator to solve some electronic problems that work a lot with polar coordinates, in this calculator representing these exercises is very easy, as shown below.

In Mathematica I have tried using "FromPolarCoordinates", but it seems to me that it is very tedious, I wanted to know if there is an easier way to represent polar coordinates. Thanks

Answer 1

Display a complex number as a phasor

Here is a bit of code that may give you some ideas about how to display numeric complex values in phasor notation.

ClearAll[phasor]
Format[phasor[z_Complex]] :=
  With[{angleSymbol = Style[FromCharacterCode[8736], 18, Bold]},
   Row[{Abs[z], Round[Arg[z]/Degree, 1] [Degree]}, angleSymbol]
  ]
z = 5 Exp[I 125 π/180];
z // N // phasor
z // phasor

The Format statement tells Mathematica how to display one particular type of expression. The expression must consist of the wrapper phasor applied to a numeric value having Complex as its head. To create the angle symbol, we start with the Mathematica symbol \[Angle] and use a font size of 18 with an appearance of Bold.

To test the Format, we assign a complex value to $z$. But, $z$ is still symbolic. We must also apply N to get the numerical value of $z$ and then apply phasor, which we have told Mathematica to display in phasor notation.

Without converting $z$ to a numeric value, Mathematica displays the wrapper applied to the expression.

Input a complex number as a phasor

First, we define a function called phasor that acts on 2 values to produce a complex-valued expression. The 2 values are the magnitude and the phase of the complex value. In this definition, we assume the phase is given in degrees.

phasor[mag_, deg_] := mag Exp[I π deg/180]
5 ~ phasor ~ 125  // N   (*  this is infix notation  *)

When phasor appears with 2 arguments, it is a function that returns a complex value. Earlier, when phasor appeared with 1 argument, it was a wrapper.

We want to be able to enter 5 \[Angle] 125 and have Mathematica recognize that as 5 ~ phasor ~ 125. To do that we need to load the Notation package.

<< Notation`

When we evaluate that expression the Notation Palette appears. We select the InfixNotation menu item. That produces an InfixNotation template that we must fill in. Now comes the tricky part. We click once on the left box (the first argument of the InfixNotation command) and type in \[Angle]. Then click once on the right box (the second argument) and type in phasor. Finally, press Shift-Enter to evaluate the InfixNotation command.

Do not try to do this without the Notation Palette, unless you are already an expert.

Now test the new notation by evaluating 5 \[Angle] 125. Be sure to include a space before the 125. It should appear as $5 \text{ }\angle\text{ } 125$ and evaluate to -2.86788 + 4.09576 I. If it works, save your notebook with the InfixNotation template already filled in.

If it doesn't work, or if you get an error when press Shift-Enter to evaluate the InfixNotation command, delete that InfixNotation command and try it again with a fresh template from the Notation Palette. The place where I always make a mistake is in clicking (just one time) on those little boxes in the InfixNotation template.