Two questions about Symbolic Complex functions.

There is no mathematical difference between 1i and i - it's just an ugly Primism. Possibly introduced as part of a Nannyware Groupthink exercise to prevent new users getting confused - mathematical convention be damned! Or it's a case of software engineers rather than scientists/mathematicians/engineers having more of say in how things should look. Whatever. Mathcad 15 does it better.  In M15, you could use a Math Style to distinguish compkex numbers by font or colour, but Prime doesn't have that option unless you want to use one of the other labels.

a+bi looks different possibly because youve typed bi, which is a legitimate name rather than an imaginary number.

Override Prime's built in abs function with abs(z):=sqrt (Re (z)^2+Im(z)^2), then call symbolically with assume, ALL=real.  The symbolic processor will otherwise have to consider the possibility that zeta and/or r is complex.

Stuart

Mathcad has always required you to input an imaginary number using "1i" or "1j" --the two keystrokes with nothing between them.  Typing "1*I" will get you either an error (if you haven't declared a variable "I", or simply your already defined variable.

Before Prime, after you typed "3+4*1i", you would see displayed "3+4i", the superfluous "1" would disappear.  As Stuart has said, Prime will display it as typed.

One could argue that this avoids the confusion of what's imaginary and what's not.  (Note that with the cursor in the expression the "1i" is still there in version 15.

For a version that claims to be more "presentation friendly," one might expect closer adherence to standard terminology.

Oh well!