The IMLOG2 function calculates the base 2 logarithm 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.
Provide an example equation of when the base 2 logarithm is needed with real values ?
This equation can be solved using the base 2 logarithm: 2x=16
becomes
log2(2x) = log2(16)
becomes
x log2(2) = 4
log2(2) = 1
x*1=4
equals
x = 4
What is the difference between the natural logarithm and the base 2 logarithm?
The natural logarithm uses e as the base and the log2 uses 2 as the base.
What is the difference between the IMLOG2 function and the IMLOG10 function?
The IMLOG2 function uses 2 as the base and the IMLOG10 function uses 10 as the base.
1. IMLOG2 Function Syntax
IMLOG2(inumber)
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2. IMLOG2 Function Arguments
| inumber |
Required. A complex number in x+yi or x+yj text format. |
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3. IMLOG2 function example
The image above demonstrates a formula in cell B28 that calculates the base 2 logarithm of a complex number specified in cell B25.
Cell C28 calculates the real number from the complex number in cell B28. Cell D28 extracts the imaginary number from the complex number specified in cell B28.
The real and imaginary numbers separated in a cell each allow us to graph the complex number on the complex plane.
Formula in cell B28:
=IMLOG2(B25)
The chart above shows the complex plane, the y-axis is the imaginary axis and the x-axis is the real axis.
Complex number 5+5i is the light blue line in the first quadrant. The base 2 logarithm of 5+5i is the green line also in the first quadrant.
3.1 Explaining formula
Step 1 - Populate arguments
IMLOG2(inumber)
becomes
IMLOG2(B25)
Step 2 - Evaluate the IMLOG2 function
IMLOG2(B25)
becomes
IMLOG2("5+5i")
and returns
2.82192809488736+1.1330900354568i
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4. How to calculate the base 2 logarithm of a complex number in detail?
The base 2 logarithm of a complex number is calculated like this:
C = x + yi
IMLOG2(C) =log2(e)ln(x+yi)
For example, C = 5 + 5i
IMLOG2(C) =log2(e)ln(x+yi) = log2(e)ln(5+5i)
IMLOG2(C) = log2(e)ln(5+5i) = 1.44269504088896*ln(5+5i)
IMLOG2(C) = 1.44269504088896*ln(5+5i) =1.44269504088896*(1.95601150271407+0.785398163397448i)
IMLOG2(C) = 1.44269504088896*(1.95601150271407+0.785398163397448i) = 2.82192809488736+1.1330900354568i
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5. The IMLOG2 function not working - #NUM error
The base 2 logarithm function IMLOG2(x+yi) is not defined for x=0, IMLOG2(0) is not a valid expression.
The IFERROR function can help you handle errors by returning a value of your choice if an error value occurs.
Why is it not possible to calculate the base 10 logarithm of a complex number that has a real part of zero and an imaginary part of 0?
The formula to calculate the base 2 logarithm of a complex number is log10(x+yi)=(log10e)ln(x+yi)
There is no solution to ln(0) which is why the calculation is not possible.
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Functions in this article
Functions in 'Engineering' category
The IMLOG2 function function is one of many functions in the 'Engineering' category.
Converts a binary number to the decimal number system.
Converts a binary number to hexadecimal.
Converts a binary number to octal.
Calculates a bitwise 'AND' of two numbers.
Calculates a number whose binary representation is shifted left by a specified number of bits.
Performs a bitwise 'OR' of two numbers.
Calculates the number where the binary equivalent is shifted right by a specified number of bits and then converted back to a number.
Calculates a decimal number that is a result of a bitwise comparison "XOR" of two numbers.
Returns a complex number based on a real and imaginary number.
Converts a number from one measurement system to another.
Converts a decimal number to a binary number.
Converts a decimal number to a hexadecimal number.
Converts a decimal number to an octal number.
Evaluates whether two numerical values are equal.
Converts a hexadecimal number to a binary number.
Converts a hexadecimal number to a decimal number.
Converts hexadecimal to octal.
Calculates the absolute value (modulus) of a complex number in x + yi or x + yj text format.
Calculates the imaginary value of a complex number in x + yi or x + yj text format.
Calculates theta θ which is an angle displayed in radians based on complex numbers in rectangular form.
Calculates the complex conjugate of a complex number in x + yi or x + yj text format.
Calculates the cosine of a complex number in x + yi or x + yj text format.
Calculates the hyperbole cosine of a complex number in x + yi or x + yj text format.
Calculates the cotangent of a complex number in x + yi or x + yj text format.
Calculates the cosecant of a complex number in x + yi or x + yj text format.
Calculates the hyperbolic cosecant of a complex number in x + yi or x + yj text format.
Calculates the quotient of two complex numbers in x + yi or x + yj text format.
Calculates the exponential of a complex number in x + yi or x + yj text format.
Calculates the natural logarithm of a complex number in x + yi or x + yj text format.
Calculates the base 10 logarithm of a complex number in x + yi or x + yj text format.
Calculates the base 2 logarithm of a complex number in x + yi or x + yj text format.
Calculates a complex number raised to a given power in x + yi or x + yj text format.
Calculates the product of complex numbers in x + yi or x + yj text format.
Calculates the real coefficient of a complex number in x + yi or x + yj text format.
Calculates the secant of a complex number in x + yi or x + yj text format.
Calculates the hyperbolic secant of a complex number in x + yi or x + yj text format.
Calculates the sine of a complex number in x + yi or x + yj text format.
Calculates the hyperbolic sine of a complex number in x + yi or x + yj text format.
Calculates the square root of a complex number in x + yi or x + yj text format.
Calculates the difference between two complex numbers in x + yi or x + yj text format.
Calculates the total of two or more complex numbers in x + yi or x + yj text format.
Calculates the tangent of a complex number in x + yi or x + yj text format.
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