IMREAL function

The IMREAL function in Excel returns the real (non-imaginary) part of a complex number.

Syntax

IMREAL(inumber)

Parameters

• inumber: This is the complex number from which you want to extract the real part. The complex number can be provided as a string in the form a + bi or a + bj, where a is the real part, and b is the imaginary part. You can also use a cell reference that contains a complex number.

How It Works

The IMREAL function extracts and returns only the real part (the coefficient of the real number) of the given complex number.

For a complex number z = a + bi:

• The real part is a, and the imaginary part is b.
• IMREAL will return the value of a (the real part) as a number.

Examples

1. Extract the Real Part of a Complex Number: To extract the real part of the complex number 3 + 4i:

   =IMREAL("3+4i")
   

   The result will be 3, which is the real part of the complex number.

2. Extract the Real Part from a Cell Reference: If cell A1 contains the complex number "2+5i", you can extract the real part using:

   =IMREAL(A1)
   

   The result will be 2.

3. Complex Number with a Negative Real Part: If the complex number is -6 + 7i, the real part is -6, so:

   =IMREAL("-6+7i")
   

   The result will be -6.

4. Purely Imaginary Number: For a purely imaginary number like "0+2i", the real part is 0, so:

   =IMREAL("0+2i")
   

   The result will be 0.

Important Notes

• The IMREAL function works only with valid complex numbers. If the input is not a valid complex number, Excel will return a #VALUE! error.
• Complex numbers in Excel can be entered with either i or j to represent the imaginary part.
• The IMREAL function only returns the real part of the complex number; it does not return the imaginary part. Use the IMAGINARY function to retrieve the imaginary part.

Summary

The IMREAL function in Excel is used to extract and return the real part of a complex number. This function is helpful when working with complex numbers in calculations that involve separating the real and imaginary components.