IMEXP in Google Sheets: Model Complex Growth and Rotation Separately

• Introduced: first introduction date is not established by the reviewed official history; no desktop release number is inferred.
• Availability: documented in the rolling Google Sheets service; these examples use the web worksheet workflow.
• Checked: October 14, 2026; official IMEXP reference. Documentation and independent models, with no native Sheets execution or wider client certification.

=IMEXP(exponent)

The input is required. Google illustrates i and j complex text and COMPLEX constructions. Its equation explicitly separates real exponential growth from angular rotation.

The imaginary coefficient y is a radian angle in that equation. The real coefficient x controls the output magnitude through EXP(x). An angle stored in degrees must be converted before it occupies that imaginary coefficient.

The dedicated page does not give a full invalid-input, blank or coercion/error table. These examples use explicit complex strings or numeric coefficients passed to COMPLEX, rather than inferring every accepted input form.

Enter only the first column as Plain text in A2:A5. Put =IMEXP(A2) in B2 and fill down. Extract the two output coefficients into C and D.

Use =IMREAL(B2) and =IMAGINARY(B2), filling down. The displayed expected numbers are independently calculated and rounded to nine decimals.

The first two inputs have the same real exponent but opposite angle signs. Their output magnitudes match, and their imaginary output signs differ. The last two keep angle 0.5 while changing the real growth coefficient.

For the first row, calculate:

=EXP(0.5)*COS(0.5)
=EXP(0.5)*SIN(0.5)

Expected results are approximately 1.446889037 and 0.790439083. A cell-driven version substitutes IMREAL(A2) and IMAGINARY(A2) for the two coefficients.

The independently expected magnitudes of B2:B5 are approximately 1.648721271, 1.648721271, one and 0.606530660. Check them with IMABS.

The magnitudes depend only on x. They are not EXP of the input magnitude: that different expression would mix direction into the growth factor.

Suppose a fictional result should have magnitude three and angle 30 degrees. Put three in F2 and 30 in G2, then enter:

=IMEXP(COMPLEX(LN(F2),RADIANS(G2)))

The independently expected coefficients are 3×SQRT(3)/2 and 1.5, approximately 2.598076211 and 1.5. The magnitude is three.

LN(3) is the required real exponent because EXP(LN(3))=3. The imaginary exponent is PI()/6 after converting 30 degrees to radians.

This construction requires a positive target magnitude for LN. Zero magnitude has no finite real exponent in the mathematical exponential model; do not treat it as a normal LN input in this workflow.

The first two table inputs add to the real quantity one. Compare:

=IMPRODUCT(IMEXP(A2),IMEXP(A3))
=IMEXP(IMSUM(A2,A3))

The independently expected result has real coefficient e, approximately 2.718281828, and imaginary coefficient zero. Multiplying the conjugate outputs cancels their imaginary cross terms.

For a second check, squaring the first exponential equals the exponential of 1+i. Both have expected coefficients approximately 1.468693940 and 2.287355287, matching Google’s explicit worked control for that input.

IMPRODUCT and IMSUM operate on the full complex quantities. Ordinary multiplication of displayed complex-looking strings is not the operation used here.

Adding 2×PI() to y describes the same output direction. The mathematical exponentials of 0+0i and 0+2×PI()i both equal one.

Construct the second input as =COMPLEX(0,2*PI()) rather than typing a literal expression inside complex text. Native trigonometric rounding may leave a tiny imaginary residual, so compare components using a declared tolerance.

This periodicity means that the original imaginary exponent cannot be uniquely recovered from IMEXP alone. Keep the source angle separately if its number of complete turns matters.

Google also documents the j-notation control =IMEXP("2-2j"), whose expected coefficients are approximately −3.074932321 and −6.718849697. A negative real output is compatible with a positive magnitude because direction matters.

For the modest examples here, 0.000000001 is an explicit component-checking tolerance, not a general service accuracy promise. Large positive real exponents can overflow and very negative ones can underflow; exact native thresholds and error displays remain unverified. No native Sheets execution was performed.

• Google IMEXP reference.
• Editorial testing standards.

Examples use fictional data, English function names and comma separators. Expected outputs are independent mathematical calculations or explicitly documented rules, not native Sheets captures. Check the spreadsheet locale when reproducing punctuation-sensitive formulas.