Purpose
Return value
Syntax
=IMABS(inumber)
- inumber - The string representing a complex number.
Using the IMABS function
The Excel IMABS function returns the absolute value of a complex number. For example:
=IMABS("4+3i") // returns 5
Excel handles complex numbers as strings formatted like “x+yi” or “x+yj”. Use the COMPLEX function to get the string representing a complex number.
Explanation
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.
=IMABS("-12-5i") // returns 13
In general, the absolute value of a complex number “z=x+yi” is given by the formula below.
=SQRT(x^2 + y^2)
Notes
- IMABS returns a #NUM error when the input does not represent a valid complex number.
Images courtesy of wumbo.net .
Purpose
Return value
Syntax
=IMAGINARY(inumber)
- inumber - The string representing a complex number.
Using the IMAGINARY function
The Excel IMAGINARY function returns the imaginary part of a complex number. For example:
=IMAGINARY("4+3i") // returns 3
Excel handles complex numbers as strings formatted like “x+yi” or “x+yj”. Use the COMPLEX function to get the string representing a complex number.
Explanation
A complex number is drawn as an arrow in the complex plane, where the horizontal axis corresponds to the real part of the number and the vertical axis corresponds to the imaginary part of the number. For example, the complex number “2-5i” is drawn below.
The IMAGINARY function returns the vertical component of the complex number.
=IMAGINARY("2-5i") // returns -5
Notes:
- IMAGINARY returns a #NUM error when the input does not represent a valid complex number.
Images courtesy of wumbo.net .
