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.