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#Engineering

IMABS

Excel Functions

Get the absolute value of a complex number

Syntax

EXCEL
=IMABS(inumber)

Arguments

Parameter Description
inumber The string representing a complex number.

Return Value

The absolute value of a complex number

Details

The Excel IMABS function returns the absolute value of a complex number. For example: The absolute value of a complex number goes by several other names: modulus, length, or magnitude. All of them refer to the same thing. When we draw the arrow representing a complex number, the absolute value is equal to the distance from the origin to the tip of the complex number. The IMABS function always returns a positive number. For example, consider the complex number "-12-5i" which points in a different direction. The absolute value of this complex number is positive 13. In general, the absolute value of a complex number "z=x+yi" is given by the formula below.

Examples

Example 1

The Excel IMABS function returns the absolute value of a complex number. For example:

EXCEL
=IMABS("4+3i") // returns 5
Explanation

The absolute value of this complex number is positive 13.

EXCEL
=IMABS("-12-5i") // returns 13
Explanation

In general, the absolute value of a complex number "z=x+yi" is given by the formula below.

EXCEL
=SQRT(x^2 + y^2)

See Also

COMPLEX IMARGUMENT IMREAL IMAGINARY