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#Engineering

IMLN

Excel Functions 🇮🇩 Bahasa Indonesia

Dapatkan bilangan kompleks log natural

Syntax

EXCEL 
=IMLN(complex_num)

Arguments

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

Return Value

Mengembalikan logaritma bilangan kompleks.

Details

Fungsi Excel IMLN mengembalikan logaritma natural bilangan kompleks. Misalnya, dengan memasukkan bilangan kompleks "3+4i", fungsi tersebut akan mengembalikan logaritma bilangan kompleks tersebut. Bagian riil dari keluaran sama dengan logaritma natural jarak dari titik asal ke titik "3+4i" pada bidang kompleks. Bagian imajiner dari keluaran sama dengan sudut dalam radian bilangan kompleks terhadap sumbu real positif. Diberikan bilangan kompleks z, logaritma kompleks didefinisikan sebagai: Di ​​Excel, logaritma kompleks sama dengan rumus berikut di mana sel B6 berisi bilangan kompleks:

Contoh

Example 1

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

EXCEL 
=IMLN(COMPLEX(3,4)) // returns 1.6094379124341 + 0.927295218001612i
Example 2

The 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.

EXCEL 
=LN(IMABS(COMPLEX(3,4))) // returns 1.609437912
Example 3

The imaginary part of the output is equal to the angle in radians of the complex number relative to the positive real axis.

EXCEL 
=IMARGUMENT(COMPLEX(3,4)) // returns 0.927295218
Explanation

In Excel, the complex logarithm is equal to the following formula where cell B6 contains a complex number:

EXCEL 
=COMPLEX(LN(IMABS(B6)),IMARGUMENT(B6))
Visualizing the Output

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.

EXCEL 
=IMREAL(IMLN(COMPLEX(3,4))) // returns 1.609437912434100
Visualizing the Output

Geometrically, the imaginary part equals the angle in radians of the complex number output by the function.

EXCEL 
=IMAGINARY(IMLN(COMPLEX(3,4))) // returns 0.927295218

See Also

COMPLEX LN IMABS IMARGUMENT