Complex Numbers Continued: Amplitude
This article assumes you have read our article on Polar Representation of a Complex Number
Resuming from there, we had determined t = tan-1(b/a), which is called the amplitude or argument of the complex number a+ib and it is denoted by amp(a+ib).
The value of t which lies in the interval (-π, π), is called the principal amplitude of the complex number a+ib. Principal amplitude of a complex number can be found as follows.
First find t = tan-1|b/a|
Then the principal amplitude is,
a) t, if both a and b are positive
b) π-t, if a is negative and b is positive
c) –( π-t), if both a and b are negative
d) –t, if a is positive and b is negative
Properties of amplitude:
For any two complex numbers Z1 and Z2,
(i) Amp(Z1 Z2) = Amp (Z1) + Amp (Z2)
(ii) Amp(Z1 /Z2) = Amp (Z1) – Amp (Z2)
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