# Default magnitude for <complex> should be 1

• To: info-dylan@cambridge.apple.com
• Subject: Default magnitude for <complex> should be 1
• From: squeegee@world.std.com (Stephen C. Gilardi)
• Date: Thu, 15 Oct 1992 23:03:53 -0400

```Dear info-dylan,

I'm a newcomer to the discussion, so please forgive me if this has

On page 148 of the Dylan book, it is specified that:

(make <complex> :angle a)

is interpreted as:

(make-polar 0 a)

The choice of 0 as the default magnitude seems to me not to be the best
one.  I think the default magnitude should be 1.

Rationale:

 As currently specified, (make <complex> :angle a) is equal to 0
regardless of a.  We don't need another fancy and confusing way to type 0.

 It is fairly common when using complex numbers to use a "pure angle"
in the sense of exp(sqrt(-1) * theta).  Defaulting the magnitude to 1
makes (make <complex> :angle theta) accomplish that.

 When humans work with complex numbers, rectangular coordinates are easy
to use in additive operations, and polar coordinates are easy to use in
multiplicative operations.  With the mangitude defaulted to 1, the
following two identities apply and there is a nice symmetry to them:

(make <complex> magnitude: a angle: b) =
(* (make <complex> magnitude: a) (make <complex> angle: b))

(make <complex> x: a y: b) =
(+ (make <complex> x: a) (make <complex> y: b))

Proposal:

Change the Dylan spec such that

(make <complex> :angle a)

is interpreted as

(make-polar 1 a)

--Steve

Stephen C. Gilardi
SQ Software
squeegee@world.std.com

```