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By Birkhoff G.D.

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A. i(t) = /,,cos(û» - л/6) b. 10 Find the instantaneous V(t) for the following phasors using a cosine reference. a. Vs = IV"" 4 b. 8 \\2-j5](V) QUATERNIONS Because of its historical significance as the mathematical language of Maxwell, the subject of quaternions should be briefly known to students of electromagnetics. As mentioned in the "Introduction," Maxwell's equations were in the form of eight field equations that explicitly contained the magnetic vector potential and 12 quaternion equations that contained magnetic mass, magnetic charge, scalar magnetic potential, magnetic charge current, and magnetic conductivity of media.

Although even symbolic simplification can be accomplished with computers, it will nonetheless be useful to become adept at doing complex algebra by hand. 7 PHASOR NOTATION In electromagnetic engineering, electric and magnetic fields that vary sinusoidally with time play a large role. In the sense that an arbitrary but otherwise periodic field can be expanded into a Fourier series of sinusoidal components and a transient nonperiodic field can be expressed as a Fourier integral, we can concentrate on analyzing steady and sinusoidal fields with the confidence that our theory can be extended to the more general situation involving nonsinusoidal time dependence.

2 If z = 3 + j4, determine following quantities in polar form. a. z3 b- И с. l/iz3! d. Re( |z'| ) e. 3 Complex numbers z\ and zi are given as zi = \§e~'m and Z2 = Se130". In polar form, determine the following: a. b. с d. 4 If two complex number are given as zi = 2 —ß and zi = 4 +j5, find the value ofln(z,)ln(z 2 ). 5 If two complex number are given as Z\ = 4 —ß and z2 = 5 +j4, find the value of eJie*"2. 3. If R = 10ΜΩ, С = lOOpF, and L = 1 H, use phasor notation to find the following: a. /(0 b.