IMCOS 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.

IMCOS returns complex cosine. For z = a+bi, cos(z) = cos(a)cosh(b) − i sin(a)sinh(b). Its magnitude can exceed 1 when the imaginary component is nonzero. It is a different operation from applying real COS separately to two components. Function help.

=IMCOS(complexValue)

Supply exactly one complex value. The examples construct values with COMPLEX(real;imaginary); accepted strings and purely real numeric inputs pass through the same complex converter. 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.

At z = i, cosine is the real value cosh(1), approximately 1.543080634815. The table therefore shows no imaginary component for that input. Compare it with cos(1), approximately 0.540302305868, to see why replacing an imaginary argument with a real one changes the problem.

A worksheet with real and imaginary inputs in A2:B2 can use =IMCOS(COMPLEX(A2;B2)). Keep the input parts and radian convention visible when interpreting a resulting sign.

Cosine is even: cos(−z)=cos(z). The executed difference between IMCOS(z) and IMCOS(−z), with z = 0.5+0.25i, returned (0,0). Both negation and subtraction used the complex functions, so neither step depends on formatted text arithmetic.

The companion identity cos²(z)+sin²(z)=1 remains valid for complex inputs. A large cosine magnitude can be balanced by a complex sine-square term; the familiar real bound of 1 does not apply to the components individually.

The exact advanced-check formula was:

=IMSUB(IMCOS(COMPLEX(0.5;0.25));IMCOS(IMSUB(0;COMPLEX(0.5;0.25))))

Invalid and empty text converted to zero in the tested engine path, so IMCOS(“abc”) returned (1,0). That plausible number does not establish that the input parsed correctly.

The exact mathematical value cos(π/2) is zero. IMCOS(PI()/2) instead had a real component near 6.123233995737E−17 because the represented angle is slightly displaced from π/2. Retain the input precision and use a suitable tolerance in checks.

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.