Purpose
Return value
Syntax
=IMTAN(complex_num)- complex_num - The complex number in the form "x+yi".
How to use
The Excel IMTAN function returns the tangent of a complex number. For example, given the complex number "3+4i" as input, the function returns "-0.000187346+0.999355987i"
=IMTAN("3+4i") // returns -0.000187346+0.999355987i
Explanation
In math, the tangent of a complex number is defined in terms of complex sine and cosine functions.
In Excel, the tangent of a complex number is equivalent to the following formula.
=IMDIV(IMSIN(z),IMCOS(z)) // equivalent to IMTAN(z)
The 3D plot below visualizes the function's real output. The horizontal XY plane represents input from the complex plane, and the vertical axis represents the function's real output.
The output along the real axis forms the shape of the regular (circular) tangent function.
The imaginary output of the function is visualized by the 3D plot below.
The output along the imaginary axis forms the shape of the hyperbolic tangent function.
Related functions
TAN Function
The Excel TAN function returns the tangent of the angle given in radians. To supply an angle to TAN in degrees, multiply the angle by PI()/180 or use the RADIANS function to convert to radians.
TANH Function
The Excel TANH function returns the hyperbolic tangent of a number.
IMCOS Function
The Excel IMCOS function returns the cosine of a complex number.
IMSIN Function
The Excel IMSIN function returns the sine of a complex number.
COMPLEX Function
The Excel COMPLEX function returns the string representation of a complex number.
