IMABS

Microsoft publishes '=IMABS("5+12i")' with the result 13. Derived independently from the definition the page states, |z| = sqrt(x^2 + y^2): sqrt(25 + 144) = sqrt(169) = 13 exactly. A Pythagorean triple was chosen by Microsoft precisely so the answer is an exact integer, so this is asserted with no ROUND wrapper -- any floating-point drift shows up immediately.

Not published on the IMABS page, but 3+4i is the complex number Microsoft's own IMAGINARY, IMARGUMENT, IMCONJUGATE and IMLN pages all use, so this ties the whole family to one number. sqrt(9 + 16) = sqrt(25) = 5 exactly.

Derived from |z| = sqrt(x^2 + y^2), which squares away both signs: sqrt(9 + 16) = 5. Included because an implementation that parses the string by splitting on the sign characters, rather than by reading a signed real and a signed imaginary part, mis-handles a leading minus.

Microsoft documents every IM* function as accepting "a complex number in x + yi or x + yj text format", so the j suffix is not an alternative spelling this corpus invented -- it is half of the documented input grammar, and an engine that parses only the i form is incompatible on documented input. Same derivation as the doc example: sqrt(25 + 144) = 13.

|i| = 1. This is the parsing edge case of the whole family: "i" carries neither a real part nor an explicit coefficient, and it is exactly the form Excel itself PRINTS for a result whose real part is 0 and whose imaginary coefficient is 1, so an engine that cannot read it back cannot round-trip its own output.

Microsoft's IMAGINARY page establishes that a bare number is a valid inumber by publishing '=IMAGINARY(4)' with the result 0. A real 4 therefore has modulus sqrt(16 + 0) = 4.

Microsoft publishes '=IMABS("5+12i")' with the result 13. Derived independently from the definition the page states, |z| = sqrt(x^2 + y^2): sqrt(25 + 144) = sqrt(169) = 13 exactly. A Pythagorean triple was chosen by Microsoft precisely so the answer is an exact integer, so this is asserted with no ROUND wrapper -- any floating-point drift shows up immediately.

Not published on the IMABS page, but 3+4i is the complex number Microsoft's own IMAGINARY, IMARGUMENT, IMCONJUGATE and IMLN pages all use, so this ties the whole family to one number. sqrt(9 + 16) = sqrt(25) = 5 exactly.

Derived from |z| = sqrt(x^2 + y^2), which squares away both signs: sqrt(9 + 16) = 5. Included because an implementation that parses the string by splitting on the sign characters, rather than by reading a signed real and a signed imaginary part, mis-handles a leading minus.

Microsoft documents every IM* function as accepting "a complex number in x + yi or x + yj text format", so the j suffix is not an alternative spelling this corpus invented -- it is half of the documented input grammar, and an engine that parses only the i form is incompatible on documented input. Same derivation as the doc example: sqrt(25 + 144) = 13.

|i| = 1. This is the parsing edge case of the whole family: "i" carries neither a real part nor an explicit coefficient, and it is exactly the form Excel itself PRINTS for a result whose real part is 0 and whose imaginary coefficient is 1, so an engine that cannot read it back cannot round-trip its own output.

Microsoft's IMAGINARY page establishes that a bare number is a valid inumber by publishing '=IMAGINARY(4)' with the result 0. A real 4 therefore has modulus sqrt(16 + 0) = 4.

Microsoft publishes '=IMABS("5+12i")' with the result 13. Derived independently from the definition the page states, |z| = sqrt(x^2 + y^2): sqrt(25 + 144) = sqrt(169) = 13 exactly. A Pythagorean triple was chosen by Microsoft precisely so the answer is an exact integer, so this is asserted with no ROUND wrapper -- any floating-point drift shows up immediately.

Not published on the IMABS page, but 3+4i is the complex number Microsoft's own IMAGINARY, IMARGUMENT, IMCONJUGATE and IMLN pages all use, so this ties the whole family to one number. sqrt(9 + 16) = sqrt(25) = 5 exactly.

Derived from |z| = sqrt(x^2 + y^2), which squares away both signs: sqrt(9 + 16) = 5. Included because an implementation that parses the string by splitting on the sign characters, rather than by reading a signed real and a signed imaginary part, mis-handles a leading minus.

Microsoft documents every IM* function as accepting "a complex number in x + yi or x + yj text format", so the j suffix is not an alternative spelling this corpus invented -- it is half of the documented input grammar, and an engine that parses only the i form is incompatible on documented input. Same derivation as the doc example: sqrt(25 + 144) = 13.

|i| = 1. This is the parsing edge case of the whole family: "i" carries neither a real part nor an explicit coefficient, and it is exactly the form Excel itself PRINTS for a result whose real part is 0 and whose imaginary coefficient is 1, so an engine that cannot read it back cannot round-trip its own output.

Microsoft's IMAGINARY page establishes that a bare number is a valid inumber by publishing '=IMAGINARY(4)' with the result 0. A real 4 therefore has modulus sqrt(16 + 0) = 4.