IMEXP

What it does

IMEXP(inumber)

IMEXP(inumber) returns e raised to a complex power, represented as complex text. Its real input coefficient controls magnitude; the imaginary coefficient controls angle in radians.

Try it

=IMEXP("0") returns "1". Mathematically IMEXP("i") has components cos(1) and sin(1), approximately 0.54030230586814+0.841470984807897i.

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. Large positive real coefficients can overflow the exponential; large negative ones can underflow. Values at imaginary multiples of a mathematical quarter turn still depend on the floating-point argument that actually arrived.

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.

For a+bi, compute u=exp(a), then the pair (u*cos(b),u*sin(b)). This is the current runtime-leaf composition. At zero, u=1, cosine is one and sine zero, so formatting returns text one. Keep component nonfinite checks and zero handling before text assembly; an arbitrary language complex-library string is not an Excel representation.

Rust code

41 imexp "IMEXP" (1, 1) [V "inumber"] |s, a, sv| { unary_complex(s, a, |z| Ok(z.exp())) }

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

Version differences

No same-input comparison between named Excel builds is recorded for this function here. The documented behaviour below is not a measurement of every Excel release.

Alternatives

IMLN is the principal logarithm; IMPOWER accepts a real exponent.

Named variants

No named variants are recorded yet.