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# IMCOT function

Returns the cotangent of a complex number.

The cotangent of a complex number can be expressed by:

cot ( a + bi ) = sin ( 2 a ) − i sinh ( 2 b ) cosh ( 2 b ) − cos ( 2 a ) cot ( a + bi ) ={ sin(2a) - i sinh(2b)} over {cosh(2b) - cos(2a)}

The result is presented in the string format and has the character "i" or "j" as an imaginary unit.

This function is available since LibreOffice 3.6.

### Syntax

IMCOT(Complex_number)

Complex_number is a complex number whose cotangent is to be calculated.

A complex number is a string expression resulting in the form "a+bi" or "a+bj", where a and b are numbers.
If the complex number is actually a real number (b=0), then it can be either a string expression or a number value.

The function always returns a string representing a complex number.
If the result is a complex number with one of its parts (a or b) equal to zero, that part is not displayed.

### Examples

=IMCOT("4-3i")
returns 0.00490118239430447+0.999266927805902i.

=IMCOT(2)
returns -0.457657554360286 as a string. The imaginary part is equal to zero, so it is not displayed in the result.

#### Technical information

This function is part of the Open Document Format for Office Applications (OpenDocument) standard Version 1.2. (ISO/IEC 26300:2-2015)

Related Topics

IMCOT wiki page.

IMTAN

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