Purpose
Return value
Syntax
=IMCOSH(complex_num)
- complex_num - The number to get the hyperbolic cosine of.
Using the IMCOSH function
The Excel IMCOSH function returns the hyperbolic cosine of a complex number. Given “1+1.5707963267949i” as input, the function returns “-5.4E-15+1.175201i” as output.
=IMCOSH(COMPLEX(1, PI()/2)) // returns -5.4E-15+1.175201i
When the function’s output is plotted over the complex plane, the real output along the real axis traces the shape of the COSH function.
=IMCOSH(COMPLEX(x, 0)) // returns COSH(x)
The imaginary output along the imaginary axis traces the shape of the COS function.
=IMCOSH(COMPLEX(0, y)) // returns COS(y)
Explanation
The function can be defined using the COSH , COS , SINH , and SIN functions.
Purpose
Return value
Syntax
=IMCOT(complex_num)
- complex_num - The complex number in the form “x+yi”.
Using the IMCOT function
The Excel IMCOT function returns the cotangent of a complex number. For example, given “3+4i” as input, the function returns “-0.000187588-1.000644392i” as output.
=IMCOT("3+4i") // returns -0.000187588-1.000644392i
Explanation
In math, the cotangent of a complex number is defined using the complex sine and cosine functions.
In Excel, the cotangent of a complex number is equivalent to the following formula.
=IMDIV(IMCOS(z),IMSIN(z)) // equivalent to IMCOT(z)
The cotangent is the reciprocal of the complex tangent function .
