# Documentation/Calc Functions/IMDIV

IMDIV

## Summary:

Calculates the result of dividing one complex number by another.

## Syntax:

IMDIV(Numerator; Denominator)

## Returns:

Returns a text string giving the complex number that results from dividing one complex number by another.

## Arguments:

Numerator is a string (in quotation marks) representing a complex number in the form a+bi or a+bj, or a reference to a cell containing that string, which is the numerator or dividend of the division operation.

Denominator is a string (in quotation marks) representing a complex number in the form c+di or c+dj, or a reference to a cell containing that string, which is the denominator or divisor of the division operation.

• If either Numerator or Denominator does not have an imaginary part (b or d equal to 0), that argument’s real part can be passed to IMDIV as a number rather than a string.
• If both real and imaginary parts of Denominator are 0, IMDIV reports an invalid argument error (Err:502).
• If either Numerator or Denominator is not a valid complex number, IMDIV reports an invalid argument error (Err:502).
• If Numerator and Denominator use different imaginary units (i or j), IMDIV returns the result using the imaginary unit of Numerator.

### Details specific to IMDIV function

For complex numbers of the form a+bi and c+di, IMDIV implements the following equation:

### General information about Calc's handling of complex numbers

 For convenience, the information in this subsection is repeated on all pages describing functions that manipulate complex numbers.

• A complex number is a number that can be expressed in the form a+bi, where a and b are real numbers and i is a symbol for the imaginary unit, such that i2=−1. a is known as the real part of the complex number and b is known as its imaginary part.
• In some disciplines using i to indicate the imaginary unit may be undesirable and, in such cases, the symbol j may be used instead. The functions provided by Calc to process complex numbers can use either i or j.
• For additional general background information, visit Wikipedia’s Complex number page.
• Within Calc, a complex number is represented as a string expression of the form "a+bi" or "a+bj", where a and b are real numbers. If the complex number happens to be a real number (b=0), then it can be represented as either a string expression or a numeric value. Complex number string expressions should not contain any space characters. Examples of valid Calc complex numbers include "2", -6, "2+3i", "3j", "12.34+56.78i", and "1e+23-1e-22j". Calc would not recognize the strings "1+j2", "i+1", and "i+j" as valid complex numbers.
• The representation of the complex numbers in strings can have up to 15 significant digits and scientific style is automatically used if needed (visit Wikipedia’s Scientific notation page for more information). The decimal delimiter in complex number string expressions is always a dot, irrespective of locale setting.

## Examples:

Formula Description Returns
=IMDIV("-238+240i";"10+24i") Here the function calculates the result of dividing the first complex number by the second. 5+12i
=IMDIV("9+8j"; "1+2i") Here the function calculates the result of dividing the first complex number by the second, using the imaginary unit of the first argument. 5-2j
=IMDIV(3; -2) Here the function calculates the result of dividing the first real number by the second. -1.5
=IMDIV(E1; E2) where cells E1 and E2 contain the complex numbers 1.2-3.4i and 5.6+7.8j respectively. Here the function calculates the result of dividing the first complex number by the second, with both entered in cells. -0.214750542299349-0.308026030368764i

IMDIV