IMCONJUGATE

Returns the complex conjugate of a complex number.

Syntax:

IMCONJUGATE(complexnumber)

complexnumber is text representing a complex number, for example as a+bi or a+bj.

IMCONJUGATE returns the complex conjugate of complexnumber - that is, if complexnumber is a+bi, it returns a-bi, as text.

Example:

IMCONJUGATE("2+3i")

returns 2-3i as text.

Application:

Calculating Complex Conjugate of Impedance for Power Factor Correction

Imagine a circuit with a load that has an impedance of Zload=20+j15 Ω. This is an inductive load, as the imaginary part is positive. Inductive loads cause the current to lag the voltage, which results in a poor power factor. To improve the power factor, a capacitor is added in parallel to the load. The impedance of the capacitor needed to achieve perfect power factor correction (a power factor of 1) is the complex conjugate of the original load's impedance, but with a negative sign.

The IMCONJUGATE function can be used to easily find the complex conjugate of the load's impedance.

Scenario: An electrical engineer is analyzing an AC circuit and needs to find the complex conjugate of several load impedances to determine the appropriate components for power factor correction.

	Load	Impedance (Complex Number)	Formula	Complex Conjugate (Z*)
	A	B	C	D
1	Motor	20+15i	IMCONJUGATE("20+15i")	20-15i
2	Heater	100+0i	IMCONJUGATE("100+0i")	100-0i
3	Transformer	50-25i	IMCONJUGATE("50-25i")	50+25i
4	Cable	1+2i	IMCONJUGATE("1+2i")	1-2i

Explanation:

The Impedance column contains the complex numbers representing the impedance of different electrical components.
The Formula column shows how the IMCONJUGATE function is used in a spreadsheet. It takes the text string of the complex number as its argument.
The Complex Conjugate column shows the result of the function. For each complex number, the sign of the imaginary part has been flipped.

By using the IMCONJUGATE function, the engineer can quickly find the complex conjugates needed to calculate the required capacitance values for power factor correction. For example, for the motor with an impedance of 20+15i Ω, the conjugate is 20−15i Ω, which tells the engineer that a capacitive reactance of 15 Ω is needed to correct the power factor. This simplifies a repetitive calculation and reduces the chance of manual error.