How to use the IMTAN function
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.
Table of Contents
1. IMTAN Function Syntax
IMTAN(inumber)
2. IMTAN Function Arguments
| inumber | Required. A complex number in x+yi or x+yj text format. |
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
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.
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
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
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.
Useful resources
Functions in 'Engineering' category
The IMTAN function function is one of 42 functions in the 'Engineering' category.
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