Purpose
Return value
Syntax
=IMLOG10(complex_num)
- complex_num - The complex number in the form “x+yi”.
Using the IMLOG10 function
The Excel IMLOG10 function returns the base-10 logarithm of a complex number. For example, given the number “0-100i” as input, the function returns “2-0.682188176920921i” as output.
=IMLOG10("0-100i") // returns 2 - 0.682188176920921i
The real part of the output is equal to the logarithm (base 10) of the complex number’s magnitude.
=LOG10(IMABS("0-100i")) // returns 2
The imaginary part of the output is equal to the angle (in radians) of the complex number divided by the natural logarithm of 10.
=IMARGUMENT("0-100i")/LN(10) // returns -0.682188177
Explanation
In math, the complex logarithm of any base can be described in terms of the natural logarithm using the change of base formula.
In Excel, we can define the base-10 logarithm using the following formula.
=IMDIV(IMLN("x+yi"),IMLN("10"))
See the IMLN function for a more in-depth explanation of the complex logarithm.
Purpose
Return value
Syntax
=IMLOG2(complex_num)
- complex_num - The complex number in the form “x+yi”.
Using the IMLOG2 function
The Excel IMLOG2 function returns the base-2 logarithm of a complex number. For example, given the “-4i” input, the function returns “2-2.2661800709136i” as output.
=IMLOG2("0-4i") // returns 2 - 2.2661800709136i
The real part of the output is equal to the logarithm (base 2) of the complex number’s magnitude.
=LOG(IMABS("-4i"), 2) // returns 2
The imaginary part of the output is equal to the angle of the complex number divided by the natural logarithm of 2.
=IMARGUMENT("-4i")/LN(2) // returns -2.266180071
Explanation
In math, the complex logarithm of any base can be described in terms of the natural logarithm using the change of base formula.
In Excel, we can define the complex base-2 logarithm using the following formula.
=IMDIV(IMLN("x+yi"),IMLN("2"))
See the IMLN function for a more in-depth explanation of complex logarithms.
