IMCONJUGATE Function in Excel
The IMCONJUGATE function returns the complex conjugate of a complex number in x + yi or x + yj text format for engineering and signal processing.
Excel
Google SheetsExcelGoogle Sheets=IMCONJUGATE(inumber)Quick Answer
IMCONJUGATE function IMCONJUGATE function returns the complex conjugate of a complex number in x+yi or x+yj format. The syntax is `=IMCONJUGATE(inumber)` where inumber is a complex number in text format.
=IMCONJUGATE(inumber)Practical Examples
Basic Complex Conjugate
Find the conjugate of a simple complex number
Negative Imaginary Part
Calculate conjugate when imaginary part is negative
Pure Imaginary Number
Find conjugate of a number with no real part
Using j Notation
Calculate conjugate with engineering notation
Complex Number from COMPLEX Function
Find conjugate of dynamically created complex number
Signal Processing Application
Calculate conjugate for frequency domain analysis
Multiplication with Conjugate
Demonstrate property: z × z* gives magnitude squared
Common Errors and Solutions
IMCONJUGATE returns #NUM! error
Invalid complex number format
Ensure the complex number is in the correct format: 'x+yi' or 'x+yj'. Check for proper syntax with + or - between real and imaginary parts.
Always format complex numbers without spaces. Use proper i or j suffix for imaginary unit.
Example:
IMCONJUGATE returns #VALUE! error
Non-text or non-complex number input
The input must be a valid complex number text string or cell reference. Use COMPLEX() to create complex numbers from separate real and imaginary parts.
Wrap complex numbers in quotes or generate using COMPLEX function for dynamic values
Example:
IMCONJUGATE returns #NAME? error
Function not available or Analysis ToolPak not enabled
In older Excel versions, enable the Analysis ToolPak add-in: File > Options > Add-ins > Analysis ToolPak. In Excel 365 and Google Sheets, it's built-in.
Verify Excel version supports engineering functions (Excel 2013+ has built-in support)
Example:
Best Practices and Advanced Tips
Mathematical Property
The complex conjugate is fundamental in complex analysis. If z = a + bi, then z* = a - bi. The conjugate has the same real part but opposite imaginary part.
Magnitude Calculation
Use IMCONJUGATE with IMPRODUCT to find the magnitude squared: =IMPRODUCT(z, IMCONJUGATE(z)). Then take the square root for the actual magnitude.
Division of Complex Numbers
To divide complex numbers, multiply numerator and denominator by the conjugate of the denominator. This removes the imaginary part from the denominator.
i vs j Notation
Mathematicians typically use 'i' for the imaginary unit, while electrical engineers use 'j' (since 'i' represents current). Excel accepts both formats.
Combining with Other Complex Functions
IMCONJUGATE works seamlessly with COMPLEX, IMREAL, IMAGINARY, IMABS, IMARGUMENT, and other engineering functions for comprehensive complex number analysis.
Real Number Conjugate
The conjugate of a real number is itself. If you apply IMCONJUGATE to '5+0i', you get '5', which is mathematically correct since the imaginary part is zero.
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Example Excel formula:
Related Formulas
The COMPLEX function converts real and imaginary coefficients into a complex number of the form x + yi or x + yj for engineering calculations.
ExcelSheetsThe IMABS function calculates the absolute value (modulus) of a complex number in x+yi or x+yj text format.
ExcelSheetsThe IMAGINARY function extracts the imaginary coefficient from a complex number in x+yi or x+yj text format.
ExcelSheetsThe IMREAL function extracts the real coefficient (real part) from a complex number in x+yi or x+yj text format.
ExcelSheets