\set ECHO None
\set c1 (1,2)::complex
\set c2 (1,1)::complex
\set c3 (3,4)::complex
\set c4 (3,8)::complex
select 1::complex as a, (1::int8)::complex as b, 1.0::complex as c;
   a   |   b   |   c   
-------+-------+-------
 (1,0) | (1,0) | (1,0)
(1 row)

select (1,2)::complex as a, -(1,2)::complex as b, ~(1,2)::complex as c;
   a   |    b    |   c    
-------+---------+--------
 (1,2) | (-1,-2) | (1,-2)
(1 row)

select :c1 + (3,4)::complex as a, 3 + :c1 as b, :c1 + 3 as c;
   a   |   b   |   c   
-------+-------+-------
 (4,6) | (4,2) | (4,2)
(1 row)

select :c1 - (3,6)::complex as a, 3 - :c1 as b, :c1 - 3 as c;
    a    |   b    |   c    
---------+--------+--------
 (-2,-4) | (2,-2) | (-2,2)
(1 row)

select :c1 * (3,5)::complex as a, 3 * :c1 as b, :c1 * 3 as c;
    a    |   b   |   c   
---------+-------+-------
 (-7,11) | (3,6) | (3,6)
(1 row)

select :c1 * (3,5)::complex as a, 3.0::double precision * :c1 as b, :c1 * 3.0 as c;
    a    |   b   |   c   
---------+-------+-------
 (-7,11) | (3,6) | (3,6)
(1 row)

select :c4 / :c1  as a, (:c4 / :c1) * :c1 = :c4 as b;
     a     | b 
-----------+---
 (3.8,0.4) | t
(1 row)

select :c4 / (2,0)::complex as a, (2,0)::complex * (:c4 / (2,0)::complex) = :c4 as b;
    a    | b 
---------+---
 (1.5,4) | t
(1 row)

select :c4 / (0,2)::complex as a, (0,2)::complex * (:c4 / (0,2)::complex) = :c4 as b;
    a     | b 
----------+---
 (4,-1.5) | t
(1 row)

select :c4 / 3 as a, 3 * (:c4 / 3) = :c4 as b;
          a           | b 
----------------------+---
 (1,2.66666666666667) | t
(1 row)

select 3 / :c4 as a, :c4 * (3 / :c4) = (3,0)::complex as b;
                   a                    | b 
----------------------------------------+---
 (0.123287671232877,-0.328767123287671) | t
(1 row)

--
-- check magnitude
--
select magnitude(:c1) as magnitude;
    magnitude     
------------------
 2.23606797749979
(1 row)

select magnitude(:c2) as magnitude;
    magnitude    
-----------------
 1.4142135623731
(1 row)

select magnitude(:c3) as magnitude;
 magnitude 
-----------
         5
(1 row)

ROLLBACK;