Its computes the principal value of the base-2 logarithm of a complex number, returning the result in rectangular form (x + yi). This is the complex analog of the standard LOG() function with base 2.
Syntax
IMLOG2(complex_number)
Argument
- complex_number (required)
A complex number in either:- « x+yi » format (mathematical convention)
- « x+yj » format (engineering convention)
Technical Background
For a complex number z = x + yi:
IMLOG2(z) = (log₂e)·IMLN(z) ≈ 1.442695041·IMLN(z)
Where:
- IMLN(z) is the complex natural logarithm
- log₂e ≈ 1.4426950408889634
Example
=IMLOG2(« 3-4i ») // Returns « 2.321928095-1.337804361i »
Additional Examples
=IMLOG2(« 1+i ») // Returns « 0.5+1.133090035i »
=IMLOG2(« -8 ») // Returns « 3+4.532360141i »
=IMLOG2(« 0+16i ») // Returns « 4+2.266180071i »
=IMLOG2(« 1024 ») // Returns « 10 » (standard real base-2 log)
Key Features
- Returns the principal value (-π < Im ≤ π)
- Maintains 9 decimal place precision
- Handles all valid complex number formats
- Consistent with real base-2 logarithm for positive reals
Error Conditions
- Returns #NUM! for:
- Invalid complex number format
- Non-numeric components
- Zero magnitude (0+0i)