What is the IMTAN function?

The IMTAN function calculates the tangent of a complex number in x + yi or x + yj text format.

The letter j is used in electrical engineering to distinguish between the imaginary value and the electric current.

1. IMTAN Function Syntax

IMTAN(inumber)

Back to top

2. IMTAN Function Arguments

Back to top

3. IMTAN function example 1

The image above demonstrates a formula in cell D3 that calculates the tangent of a complex number in general or rectangular form specified in the function.

The IMTAN probably stands for imaginary tangent.

3.1 What are complex numbers?

Complex numbers allow us to solve equations that have no real solutions. Complex number have two parts, a real part and an imaginary part called i which means imaginary and stands for the square root of -1.

Link: How are complex numbers used in real life?

3.2 What are the applications for complex numbers?

Complex numbers are very useful in many fields of mathematics and science.

• Electronics: Complex numbers are used to analyze circuits that involve alternating current (AC) or signals modulated by electromagnetic waves.
• Electromagnetism: Complex numbers are used to describe the electric and magnetic fields in terms of their magnitude and direction.
• Control theory: Complex numbers are used to design and optimize systems that have feedback loops, such as robots, airplanes, or rockets.
• Signal analysis: Complex numbers are used to perform Fourier transforms, which are methods of decomposing a signal into its frequency components.
• Relativity: Complex numbers are used to express the space-time interval in special relativity, which is a measure of the distance between two events that occur in different locations and times.
• Fluid dynamics: Complex numbers are used to model the flow of fluids, such as air or water.

Link: Complex number - Wikipedia

Back to top

4. How is the IMTAN function result calculated?

z - complex number: 1+1i
a - real number: 1
b - imaginary number: 1

The math formula to calculate the imaginary tangent is:

Step 1 - Calculate real sin

The SIN function calculates the sine of an angle.

Function syntax: SIN(number)

sin(2a)

becomes

sin(2*1)

and returns 0.909297426825682

Step 2 - Calculate real cos

The COS function calculates the cosine of an angle.

Function syntax: COS(number)

cos(2a)

becomes

cos(2*1)

and returns -0.416146836547142

Step 3 - Calculate imaginary sinh

The SINH function calculates the hyperbolic sine of a number.

Function syntax: SINH(number)

sinh(2b)

becomes

sinh(2*1)

and returns 3.62686040784702

Step 4 - Calculate imaginary cosh

The COSH function calculates the hyperbolic cosine of a number.

Function syntax: COSH(number)

cosh(2b)

becomes

cosh(2*1)

and returns 3.76219569108363

Step 5 - Divide first quotient

0.909297426825682/(-0.416146836547142+3.76219569108363)

becomes

0.909297426825682/3.34604885453649

and returns 0.271752585319512

Step 6 - Divide second quotient

3.62686040784702/(-0.416146836547142+3.76219569108363)

becomes

3.62686040784702/3.34604885453649

and returns 1.08392332733869i

The calculations match the result from the IMTAN function.

Back to top

5. IMTAN function example 2 - cell reference

The image above demonstrates a formula in cell D3 that calculates the tangent of a complex number specified in cell C3.

Formula in cell D3:

5.1 Explaining formula

Step 1 - Populate arguments

IMTAN(inumber1)

becomes

IMTAN(C3)

Step 2 - Evaluate the IMTAN function

IMTAN(C3)

becomes

IMTAN("1+1i")

and returns

0.271752585319512+1.08392332733869i

Back to top

6. IMTAN function example 3 - real and imaginary coefficients

The image above demonstrates a formula in cell D3 that calculates the tangent of real and imaginary coefficients specified in the COMPLEX function. The COMPLEX function lets you create a complex number using a real and imaginary number.

Formula in cell D3:

6.1 Explaining formula

Step 1 - Calculate complex number based on a real and imaginary number

The COMPLEX function returns a complex number based on a real and imaginary number.

Function syntax: COMPLEX(real_num, i_num, [suffix])

COMPLEX(3,2)

returns

"3+2i".

Step 2 - Calculate the tangent of a complex number

IMTAN(COMPLEX(3,2))

becomes

IMTAN("3+2i")

and returns

-0.009+ 0.965i

Back to top

7. IMTAN function error

The IMTAN function returns a #NUM error if we use an invalid argument. Make sure the argument is valid.

The IMTAN function returns #NUM error if the suffix is not "i" or "j", or omitted.

Back to top

Useful resources

IMTAN function - Microsoft

Imaginary and Complex Numbers