## Complex numbers in Electrical Enginnering

## Complex numbers in Electrical Enginnering

(OP)

Why use complex numbers to represent amplitude and phase of AC.

How does appears in mathematical equations?

I know about Euler Formula.

Why do not we use matrixs?

How does appears in mathematical equations?

I know about Euler Formula.

Why do not we use matrixs?

## RE: Complex numbers in Electrical Enginnering

edit:

~~Can't find a link to the video right now.~~Look for 'Essense of Linear Algebra' (a series) on the

3Blue1Brownchannel on YouTube.## RE: Complex numbers in Electrical Enginnering

## RE: Complex numbers in Electrical Enginnering

For example, take a three phase system, where each of three wires measures 120 Volts RMS to neutral/ground.

But the voltage measured between them is 208 Volts RMS.

The math only works out if you take into account the phase angles involved.

## RE: Complex numbers in Electrical Enginnering

haveto use complex numbers. The basic way is to use differential equations. These are hell to solve, though. By transforming the equations into the complex symbolic space, they turn into normal algebraic equations that are much easier to work with.## RE: Complex numbers in Electrical Enginnering

CR

"As iron sharpens iron, so one person sharpens another." [Proverbs 27:17, NIV]

## RE: Complex numbers in Electrical Enginnering

Usually in a Cartesian plane the abscissa is what is called "real" like resistance and active power and on ordinate the reactance or reactive power. You may expand the area and use other way.

For instance if you have 3 balanced voltages[R,Y,B] you may take R as basis and consider VR=V+j0 then VY=V.cos(-120o)+jV.sin(-120o)=VY=-0.5.V-j0.866.V and VB=-0.5.V+j0.866.V.

By using complex number all the electrical calculations are simplified [ like load, short-circuit or voltage drop calculation].

They are more sophisticated complex number functions as Hankel function for instance, but they are not usually in the electrical engineering calculations.

A Microsoft Excel spreadsheet presents built-in complex functions as IMSUM,IMSUB,IMPRODUCT IMDIV and other in order to facilitate the complex number mathematics.

## RE: Complex numbers in Electrical Enginnering

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## RE: Complex numbers in Electrical Enginnering