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Exponential form : From Euler's equation, we have
(1.17)
A rotating vector as shown in
Figure 1.3
can be expressed as
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(1.18)
where A is the magnitude, 
is the orientation and j = 
is the imaginary number. Equation (1.18) can also be written as
(1.19)
with
(1.20)
where z is the complex sinusoid, x is the real component and y is the imaginary component.