The `IMARGUMENT` function in Excel is used to calculate the argument (or angle) of a complex number expressed in radians. The argument of a complex number is the angle formed with the positive real axis in the complex plane.
Syntax
IMARGUMENT(inumber)
- inumber: This is a required argument. It is the complex number for which you want to find the argument. The complex number can be input as a text string like “x+yi” or “x+yj”, or by using the `COMPLEX` function to convert real and imaginary coefficients into a complex number.
Returns
The `IMARGUMENT` function returns the angle in radians between the positive real axis and the line representing the complex number in the complex plane. The result is a real number.
Usage
=IMARGUMENT("3+4i")
=IMARGUMENT(COMPLEX(3, 4))
- Direct Input:
- If you have a complex number like “3+4i”, you can directly input it into the function:
- This will return the angle in radians formed with the positive x-axis.
- Using `COMPLEX` Function:
- If you have separate real and imaginary coefficients, use the `COMPLEX` function to create the complex number:
- This also calculates the argument for the complex number 3 + 4i.
Example
Suppose A1 contains the coefficient 3 (real part) and A2 contains 4 (imaginary part):
=IMARGUMENT(COMPLEX(A1, A2))
- Convert them to a complex number and calculate the argument:
Note
=DEGREES(IMARGUMENT("3+4i"))
- The function returns results in radians. If you need the angle in degrees, you can use the `DEGREES` function to convert the result:
Keep in mind that complex numbers in Excel can be represented in either Cartesian form (x + yi) or polar form, and handling complex numbers in spreadsheet calculations can be quite efficient with functions like `IMARGUMENT`.
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