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First of tell me what is amplitude is it argument .then my question is if 0

First of tell me what is amplitude is it argument .then my question is if 0

Grade:11

1 Answers

manna
59 Points
7 years ago
To find the Amplitude or Argument of a complex number let us assume that, a complex number z = x + iy where x > 0 and y > 0 are real, i = √-1 and x22 + y22 ≠ 0; for which the equations x = |z| cos θ and y = |z| sin θ are simultaneously satisfied then, the value of θ is called the Argument (Agr) of z or Amplitude (Amp) of z.

From the above equations x = |z| cos θ and y = |z| sin θ satisfies infinite values of θ and for any infinite values of θ is the value of Arg z. Thus, for any unique value of θ that lies in the interval - π
We know that, cos (2nπ + θ) = cos θ and sin (2nπ + θ) = sin θ (where n = 0, ±1, ±2, ±3, .............), then we get,
Amp z = 2nπ + amp z where - π
 
if it is 0 then it depends \theta will lie between 0 to \pi

 

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