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Now the magnitude of the current regardless of its phase is 7.6945A. These are real
coulombs moving around here. Real electrons or 7.6945 coulombs/sec through the
resistance so we can drop the phase angle. The power radiated by the resistance is
only determined by the current through that resistance.

The true power is a lot less than the apparent power calculated earlier. Apparent
power is 796VA while true power is 414W.

We do not use the term power factor (PF) in radio. PF is just the ratio between true
power ÷ apparent power. When the PF=1 the true and the apparent power is the
same. At least that is what electrical engineers use. What radio engineers say (when
PF=1) is "we have resonance" - there is no reactance in the circuit.

PERFORMING CALCULATIONS WITH COMPLEX NUMBERS

Complex numbers can be added, subtracted, multiplied and divided along with other
operations, provided the rules for using complex numbers are followed. However,
using complex numbers manually is not hard, but it is cumbersome and, as such,
prone to errors. Most modern scientific calculators will perform complex number
arithmetic. There is computer software for using complex numbers and also many
scientific calculators.

My choice for doing complex number arithmetic is the scientific calculator. Some
calculator brands and models are better than others in terms of ease of use and
price. The calculator that I recommend to students is the CASIO FX-991ES-PLUS
or any similar model. This is a low-price range calculator, and unless you are a very
advanced mathematician, you are unlikely to outgrow it.

Performing complex arithmetic on the calculator is easy to learn. Once you set the
mode of the calculator to CMPLX (complex) using the mode switch, you can, with a
couple of simple rules, just key in the complex numbers and perform operations on
them returning a complex result.

WHY LEARN HOW TO USE COMPLEX NUMBERS

Most of the radio circuits we use in radiocommunications require complex numbers
to describe them. You are probably already using complex numbers if you have an
antenna analyser. Most antenna analysers will give you an impedance in rectangular
form R+/-X.

The rules for finding total impedance in series and parallel circuits are the same as
for resistance.
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