IMTAN Function (Calligra Sheets)

• Introduced: First release not established; the name is present in Calligra 2.4.0 source.
• Supported in: Calligra Sheets 26.08.2, with no retirement established.
• Scope: Desktop Sheets with the Engineering module. Examples use English semicolon-separated formulas.
• Checked: October 14, 2026. Formulas were executed through the official 25.04.2 engine library and checked against source and independent mathematics. This is not GUI-cell or workbook-import evidence; 26.08.2 was source-checked, not executed.

IMTAN returns tan(z), mathematically sin(z)/cos(z) wherever the denominator is nonzero. Complex tangent can have real and imaginary components even when a real tangent analogy is tempting. Its poles occur at real z = π/2 + kπ for integer k. Function help.

=IMTAN(complexValue)

Exactly one complex argument is required. Construct both components with COMPLEX(real;imaginary) when working from numeric cells. A numeric argument is purely real; angles are in radians. Registration and implementation, with versioned help.

Results are shown as (real,imaginary) component pairs, rounded to twelve decimal places, not a literal cell format. Tiny or very large values use thirteen significant digits in scientific notation. A component rounded to zero is shown as 0; the stored value may still contain a tiny residual or signed zero. NaN means not-a-number; infinity and NaN are not finite results.

For z = i, tan(i) = i tanh(1), approximately 0+0.761594155956i. The imaginary part is positive even though there is no real input angle. The table also shows the sign changes from conjugate and negated arguments.

With the components in A2:B2, =IMTAN(COMPLEX(A2;B2)) preserves the intended complex input. Do not replace this by TAN(A2)/TAN(B2), which has neither the same definition nor the same domain.

For z = 0.5+0.25i, the executed difference between IMTAN(z) and IMDIV(IMSIN(z);IMCOS(z)) had zero real component and imaginary residual about −2.710505431214E−20. It confirms the quotient relation for this ordinary case, allowing for finite precision.

On the imaginary axis tan(ib)=i tanh(b), which stays below magnitude 1 for finite real b. That special-axis behavior is not a bound on complex tangent everywhere: near a real pole the magnitude can be very large.

The exact advanced-check formula was:

=IMSUB(IMTAN(COMPLEX(0.5;0.25));IMDIV(IMSIN(COMPLEX(0.5;0.25));IMCOS(COMPLEX(0.5;0.25))))

IMTAN(PI()/2) returned a large finite real component, approximately 1.633123935320E16. The exact function has a pole at mathematical π/2; the finite value reflects the rounded input’s distance from that pole and must not be treated as a finite exact tangent at the pole.

Invalid or empty text became complex zero, and its tangent became zero without an engine error flag. Wrong argument counts did produce #VALUE!. These are different failure modes.

The complex conversion helper explains the text and Boolean cases above. The inspected Engineering module and complex converter are byte-identical between 25.04.2 and 26.08.2. That source comparison does not establish every locale, import path or extreme-value case.

Use COMPLEX to construct values from numeric components, IMABS for magnitude, and IMARGUMENT for principal phase.