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#Engineering

IMCONJUGATE

Excel Functions

Get the complex conjugate of a complex number

Syntax

EXCEL 
=IMCONJUGATE(inumber)

Arguments

Parameter Description
inumber The complex number in the form "x+yi".

Return Value

The complex number with the sign of the imaginary part flipped

Details

The Excel IMCONJUGATE function returns the conjugate of a complex number. For example, given the complex number "3+4i" as input, the function returns "3-4i" as output. The conjugate of a complex number has the same real part and flips the sign of the imaginary part. If a complex number is written as "x + yi", its conjugate equals "x - yi". Typically, the conjugate appears in text with a horizontal bar over the complex number. The conjugate is used to divide a complex number by another. For example, let's say you want to divide the complex number "x+yi" by another complex number "a+bi". We can convert this expression into a multiplication problem by multiplying the numerator and numerator by the conjugate of "a+bi". In other words, the divisor is converted into a real number which we know h

Examples

Example 1

The Excel IMCONJUGATE function returns the conjugate of a complex number. For example, given the complex number "3+4i" as input, the function returns

EXCEL 
=IMCONJUGATE("3+4i") // returns "3-4i"
Explanation

In other words, the divisor is converted into a real number which we know how to divide by. This is equal to the following formula in Excel.

EXCEL 
=IMPRODUCT(
    "x+yi",
    IMCONJUGATE("a+bi"),
    COMPLEX(1/IMREAL(IMPRODUCT("a+bi", IMCONJUGATE("a+bi"))), 0)
)
Explanation

In practice, Excel provides the IMDIV function to perform complex division.

EXCEL 
=IMDIV(COMPLEX(-11,29),COMPLEX(2,3)) // returns 5+7i

See Also

COMPLEX IMDIV IMREAL IMAGINARY