## 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.