The IMABS function in Excel provides a straightforward way to obtain the absolute value, or modulus, of a complex number. This mathematical operation is essential for various calculations in fields such as engineering, physics, and finance, where complex numbers frequently arise.

Syntax

IMABS(inumber)

• inumber: This parameter represents the complex number for which the absolute value is requested. The number must be in text format, following the structure “a+bi” or “a-bi”, where “a” and “b” are real numbers.

Example #1

=IMABS("3+4i")

This function call calculates the absolute value of the complex number 3 + 4i. The result of this calculation would be 5, as the modulus is determined by the formula √(a² + b²).

Example #2

=IMABS("1-1i")

Here, the function computes the modulus of the complex number 1 – 1i. The absolute value resulting from this function would be approximately 1.4142, derived from √(1² + (-1)²).

Example #3

=IMABS("0+2i")

This expression finds the absolute value of 0 + 2i. The result is 2, as the calculation simplifies to √(0² + 2²).

Error handling

• VALUE!: This error occurs when the input is not recognized as a valid complex number. Ensure that the input adheres to the proper “a+bi” format.
• NUM!: This error signifies that the function encountered a numerical issue, often arising when the imaginary part is not a number. Verify that both parts of the complex number are numerical values.

Conclusion

The IMABS function in Excel is an invaluable tool for any user dealing with complex numbers. By easily providing the absolute value, it streamlines calculations across various disciplines, enhancing both productivity and accuracy when working with mathematical models that incorporate complex numbers.