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#Engineering

IMLOG2

Excel Functions

Get base-2 log of a complex number.

Syntax

EXCEL 
=IMLOG2(complex_num)

Arguments

Parameter Description
complex_num The complex number in the form "x+yi".

Return Value

The logarithm of the complex number.

Details

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. The real part of the output is equal to the logarithm (base 2) of the complex number's magnitude. The imaginary part of the output is equal to the angle of the complex number divided by the natural logarithm of 2. 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.

Examples

Example 1

The Excel IMLOG2 function returns the base-2 logarithm of a complex number. For example, given the "-4i" input, the function returns "2-2.266180070913

EXCEL 
=IMLOG2("0-4i") // returns 2 - 2.2661800709136i
Example 2

The real part of the output is equal to the logarithm (base 2) of the complex number's magnitude.

EXCEL 
=LOG(IMABS("-4i"), 2) // returns 2
Example 3

The imaginary part of the output is equal to the angle of the complex number divided by the natural logarithm of 2.

EXCEL 
=IMARGUMENT("-4i")/LN(2) // returns -2.266180071
Explanation

In Excel, we can define the complex base-2 logarithm using the following formula.

EXCEL 
=IMDIV(IMLN("x+yi"),IMLN("2"))

See Also

IMLN IMLOG10 LOG