IMLN

What it does

IMLN(inumber)

IMLN(inumber) returns the principal natural logarithm of a nonzero complex value. The real component describes magnitude and the imaginary component describes angle.

Try it

=IMLN("i") gives about "1.5707963267949i". The modulus is one, so the real logarithm component is zero; the positive imaginary axis supplies phase pi/2. =IMLN("1") returns text zero.

Quirks

Complex arguments may be real numbers or text such as "2-3i". Use lowercase i or j; operands in one call must agree on the suffix. The current parser rejects malformed complex text with #NUM! and logical values with #VALUE!. A complex result is text, so ordinary worksheet arithmetic does not automatically treat it as a pair of numeric components. Zero has no finite logarithm and the current kernel gives #NUM!. Principal angles create a branch cut on the negative real axis; a real-valued LOG call cannot replace this function.

How to implement

Parse the two coefficients and suffix before doing arithmetic; use the common complex formatter afterward. Retain suffix consistency, suppress a zero component and omit the coefficient one before the imaginary unit. Formatting and parsing have their own fifteen-significant-digit rules, so testing only the algebra misses observable behaviour.

Compute a scaled modulus h=hypot(a,b) and principal angle theta=atan2(b,a). Reject h=0. Form the natural-log pair (ln(h),theta). Return those two components. The current code uses runtime log and atan2 leaves. This mathematical composition does not identify all their rounding stages in Excel. In particular, preserve negative-real and signed-zero boundary tests rather than assuming that every logarithm wrapper shares IMARGUMENT’s ratio route.

Rust code

42 imln "IMLN" (1, 1) [V "inumber"] |s, a, sv| { unary_complex(s, a, |z| z.ln()) }

No implementation has been published with a Handbook test suite for this function.

Version differences

The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.

The record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.

Recorded environments and comparison details.

Alternatives

IMEXP is the exponential companion; IMABS and IMARGUMENT expose the polar ingredients.

Named variants

No named variants are recorded yet.