Get natural log complex number
=IMLN(complex_num)| Parameter | Description |
|---|---|
complex_num |
The complex number in the form "x+yi". |
The Excel IMLN function returns the natural logarithm of a complex number. For example, given the complex number "3+4i" as input, the function returns
=IMLN(COMPLEX(3,4)) // returns 1.6094379124341 + 0.927295218001612iThe real part of the output is equal to the natural logarithm of the distance from the origin to the point "3+4i" in the complex plane.
=LN(IMABS(COMPLEX(3,4))) // returns 1.609437912The imaginary part of the output is equal to the angle in radians of the complex number relative to the positive real axis.
=IMARGUMENT(COMPLEX(3,4)) // returns 0.927295218In Excel, the complex logarithm is equal to the following formula where cell B6 contains a complex number:
=COMPLEX(LN(IMABS(B6)),IMARGUMENT(B6))Geometrically, the real part of the function's output equals the natural logarithm of the distance from the origin to the point in the complex plane.
=IMREAL(IMLN(COMPLEX(3,4))) // returns 1.609437912434100Geometrically, the imaginary part equals the angle in radians of the complex number output by the function.
=IMAGINARY(IMLN(COMPLEX(3,4))) // returns 0.927295218