\set ECHO None
--
-- check norm.
--
\set r1 (2,0)::complex
\set r2 (0,2)::complex
\set r3 (-2,0)::complex
\set r4 (0,-2)::complex
select norm(:r1) as a, norm(:r2) as b, norm(:r3) as c, norm(:r4) as d;
   a   |   b   |   c    |   d    
-------+-------+--------+--------
 (1,0) | (0,1) | (-1,0) | (0,-1)
(1 row)

select :r1 = magnitude(:r1)::float8 * norm(:r1) as a,
    :r2 = magnitude(:r2)::float8 * norm(:r2) as b,
    :r3 = magnitude(:r3)::float8 * norm(:r3) as c,
    :r4 = magnitude(:r4)::float8 * norm(:r4) as d;
 a | b | c | d 
---+---+---+---
 t | t | t | t
(1 row)

ROLLBACK;