IMREAL

Returns the real part of a complex number.

Syntax:

IMREAL(complexnumber)

complexnumber is text representing a complex number, for example as a+bi or a+bj, where a is the real part and b the imaginary part.

IMREAL returns the real part as a number.

Example:

IMREAL("4+3i")

returns 4.

Application:

Electrical Engineering

In electrical engineering, complex numbers are used to represent impedance in AC (alternating current) circuits. Impedance is the total opposition a circuit presents to an alternating current. It's composed of two parts: resistance and reactance.

Resistance (R): The real part, which represents the opposition to current flow that dissipates energy as heat.
Reactance (X): The imaginary part, which represents the opposition to current flow that stores and releases energy in electric and magnetic fields.

The impedance (Z) of a circuit is expressed as a complex number: Z=R+jX (engineers often use 'j' instead of 'i' to avoid confusion with current, which is also denoted by 'i').

Let's say an engineer is working with a spreadsheet that lists the impedance of various components in a circuit. They need to isolate the real part (resistance) to calculate the power dissipated by each component.

Here's how they would use the IMREAL function:

	Component	Impedance (Z)	Resistance (R)
	A	B	C
1	Resistor 1	10+0j	IMREAL(A1)
2	Inductor 1	5+20j	IMREAL(A2)
3	Capacitor 1	2-15j	IMREAL(A3)
4	Series Circuit	12+5j	IMREAL(A4)

In this table:

Column A contains the impedance of each component as a complex number (text string).
Column B uses the IMREAL function to extract the real part.
- The formula =IMREAL(A1) would return 10.
- The formula =IMREAL(A2) would return 5.
- The formula =IMREAL(A3) would return 2.
- The formula =IMREAL(A4) would return 12.

By using the IMREAL function, the engineer can quickly and accurately extract the resistance value for each component, which can then be used in other formulas to calculate things like power loss (P=I2R). This automates a crucial step in their analysis and reduces the risk of manual errors.