5.3 Complex Numbers and Complex Arithmetic cont.

Multiplication and division in rectangular form:

If A = a + jb and B = c + jd then

AB = (a + jb)(c + jd)

= (ac - bd) + j(ad + bc) and

A/B = (a + jb)/(c + jd)

= [(ac + bd) + j(bc - ad)]/(c2 + d2)

Also, the conjugate of a phasor A = a + jb = C/q is

A* = a - jb = C/-q so that AA* = (a + jb)(a - jb)

= a2 + b2 = C2 also …

1 = +1 + j0 = 1/0 ; -1 = -1 + j0 = 1/±180°

and j = 0 + j1 = 1/90°

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