1 + i

The title of this article is not correct because of technical limitations. The correct title is actually $1+i$.

$1+i$ is an esoteric programming language by user:raiseafloppafan7741 in 2026. It is based on 14 and SELECT. with the number of focus being the complex number $i$, since I is taken.

Commands

Command	Description
i	Pushes the imaginary number $i$, the square root of -1.
c	Complex conjugate of the top of the stack.
l	Principal complex natural logarithm.
e	$e^{x}$.
+	Addition. The second number popped is to the left of the operator.
*	Multiplication. The second number popped is to the left of the operator.
/	Reciprocal.
^	Exponentiation. The second number popped is the base. $0^{0}$ is defined to be 1.
>	Pops two real numbers b and a, and if a > b then 0 is pushed, otherwise 1. Imaginary/complex numbers halt the program.
<	Pops two real numbers b and a, and if a < b then 0 is pushed, otherwise 1. Imaginary/complex numbers halt the program.
[]	Defines a function.
?	Pops a decider value x, then retrieves two functions f and g. If x is zero, then g is invoked, otherwise f is. If either operand is not a function, then the program halts only when the non-function is invoked. This means that i[]i? does not halt due to an error, but []ii? does.
%	Swap the front and the back elements of the stack.
:	Duplicates the top of the stack.
(	Rolls the stack left. 4 3 2 1 (LTR) becomes 3 2 1 4.
)	Rolls the stack right. 4 3 2 1 (LTR) becomes 1 4 3 2.
$	Discards the top of the stack.
A	Read a byte from standard input. EOF returns $i$.
B	Read an integer from standard input.
C	Read a real number from standard input.
D	Read a complex number from standard input.
p	Pop the top of the stack and print it as a complex number. Real numbers print as real numbers, imaginary numbers print like you'd expect ($2i$ prints as 2i for example), and complex numbers print as a + bi.
o	Pop the top of the stack and print the two bytes associated with it. The real part is printed modulo 256, and the imaginary part is outputted only if the coefficient is greater than or equal to 256. For example, $1+i$ outputs byte 1, while $256+256i$ outputs 0 and 0. Non-integers are floored.

Mismatched value type errors halt the program.

Building blocks

This section lists some "building blocks" that can be used to make programs in $1+i$.

Constants

The constants are illustrated in this nice table format so you can easily compare the lengths of their "expressions". Only the shortest known "expressions" are listed here.

Value	Expression	Length
Imaginary
-2i	ic:+	4 (shortest possible)
-i	ic	2 (shortest possible)
Integers
-2	ii*:+	5
-1	ii*	3 (shortest possible)
0	iic+	4 (shortest possible)
1	ici*	4 (shortest possible)
2	ici*:+	6
3	ici*::++	8
4	ii+:c*	6
5	ici*::+:++	10
6	ici*::++:+	10
7	ici*:::++:++	12
8	ii+:c*:+	8
9	ii+i+:c*	8
10	ici*::+:++:+	12
11	ici*:::+:++:++	14
12	ii+:c*::++	10
13	ici*:::++:+:++	14
14	ici*:::++:++:+	14
15	ii+:c*:*ii*+	12
16	ii+:c*:*	8
17	ii+:c*:*ici*+	13
18	ii+i+:c*:+	10
19	ii+:c*::*+ii*+	14
20	ii+:c*::*+	10
21	ii+:c*::*+ici*+	15
22	ici*:::+:+++:+	14
23	ii+:c*::++:+ii*+	16
24	ii+:c*::++:+	12
25	ici*::+:++:*	12
26	ici*:::++:+:++:+	16
27	ici*::++:^	10
28	ici*:::++:++:+:+	16
29	ici*::++::^+ii*+	16
30	ici*::++::^+	12

Real and imaginary parts

The real part of a number can be retrieved with:

:c+ici*:+/*

And the imaginary part can be retrieved with:

ic*:c+ici*:+/*

These are from translations from SELECT. which uses the same mechanisms.

Nth roots

Square root

ici*:+/^

Cube root

ici*::++/^

Fourth root

ii+:c*/^

Fifth root

ici*::+:++/^

Sixth root

ici*::++:+/^

For a stack with the top two elements being a n, getting the nth root of a can be done as follows:

/^

Modulus

This one works by using $\left|z\right|={\sqrt {z{\overline {z}}}}$ which also produces the modulus.

:c*ici*:+/^

Examples

Print the language's name

ici*i+p

The output is 1 + i.

A+B Problem

It's not like the other A + B problem programs! It takes in two complex numbers and adds them.

DD+p

Truth-machine

Only accepts 1.

[$$[(:p)i?]i?][$$p]C:)ii*+?

Cat program

[][(oA:)ic+?]A:)ic+?