prime:polrec

# Polar/Rectangular

Polar coordinates are entered using R∠Angle, where ∠ is Shift-x (multiply). Rectangular coordinates are entered using complex values as in a+b*i (where i is Shift-2). Also useful is the π symbol (shift-3).

In the geometry app you can enter a point in either form using the point() function.

If you enter a polar coordinate as in 1∠(π/4), and hit enter, and then hit the ∠ button again, it'll convert the number to it's rectangular/complex form.

Note that if your system is set to radians by default, you can enter degrees by using shift-units and from the units menu, select angle-deg and the value will appear as 30_deg for example. if you type 1∠30_deg and hit enter, it'll convert automatically to 1∠0.5325… (radians). To enter a point this way in the geometry app, you cannot enter point(1∠30_deg), but you can enter 1∠30 on the home view and hit enter to convert to radians. Then, in the geometry app, you can enter point() and select menu-copy_from_home and select the radian version to put it in the point call. You can alternatively enter point(EXPR(“1∠30_deg”)).

The following function is a useful one to have in your arsenal. It will convert from polar to rectangular and vice versa…automatically.

EXPORT POLREC(Z) // POLAR/RECT CONVERT
BEGIN
LOCAL T,A,B;
T:=STRING(Z);
IF INSTRING(T,"∠") THEN
// POLAR
A:=RE(Z);
B:=IM(Z);
RETURN EXPR(A "+" B*i);
ELSE
// RECTANGULAR
A:=ABS(Z);
B:=ARG(Z);
RETURN EXPR(A "∠" B);
END // IF...
END // BEGIN