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.
Purpose
Return value
Syntax
=IMPOWER(inumber,number)
- inumber - A complex number.
- number - Power to raise number.
Using the IMPOWER function
The Excel IMPOWER function returns a complex number raised to a given power. The complex number is input as text, and must be in the form x + yi or x + yj.
For example:
=IMPOWER("1+2i",2) // returns "-3+4i"
In the example shown, the formula in D6, copied down, is:
=IMPOWER(B6,C6)
Notes:
- Only lowercase “j” and “i” are accepted by IMPOWER. Other values will result in the #NUM error.
- The number argument must be numeric
