Numbers a+bi with i²=-1 represent amplitude and phase together in AC and wave analysis.
A complex number z=a+bi has real part a and imaginary part b. Engineers write j for i. Addition is componentwise, multiplication uses j²=-1, and the conjugate a-bi gives ‖z‖²=z·z̄. They compactly represent amplitude and phase.
(2+3j)(1-j)=2-2j+3j+3 = 5+j.
Complex numbers let one symbol carry both amplitude and phase, which turns sinusoidal analysis into algebra.
Numbers a+bi with i²=-1 represent amplitude and phase together in AC and wave analysis.
Complex numbers let one symbol carry both amplitude and phase, which turns sinusoidal analysis into algebra.
The letter i is reserved for current, so engineers write j for the square root of minus one.
It is the length of the number in the complex plane, the square root of a squared plus b squared for a plus bi.
Typical applications include representing an AC impedance as R plus jX, describing the response of a filter at one frequency and computing the total current in parallel branches.
Study "Sequences and series" first (topic 21 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
Argand diagram plots a vs b. Division uses the conjugate. Roots of real polynomials come in conjugate pairs.
(2+3j)(1-j)=2-2j+3j+3 = 5+j.
The next topic is "Polar and exponential forms", which builds directly on this one.
It is classed as Beginner in Engineering Mathematics (topic 22 of 104). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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