Question

what is called the principal value of the argument?

Answer 1

. arg(12 + 9i) is the angle Θ such that tan Θ = 9/12 = 3/4,
so arctan 3/4 = 0.6435 radians

Answer 2

but this is the definition of the argument & I wanna know about its principal value.

Answer 3

In mathematics, arg is a function operating on complex numbers (visualised as a flat plane). It gives the angle between the line joining the point to the origin and the positive real axis, shown as φ in figure 1 opposite, known as an argument of the point (that is, the angle between the half-lines of the position vector representing the number and the positive real axis).

Answer 4

@maheshmeghwal9 , basically any complex number is a point on the circle

Argument is the angle made by the complex number with respect to the positive x -axis
Here
theta-->Principal argument
theta + (2pi)n -->All other possible arguments where n--->integer

Answer 5

does its value lies between [-pi,+pi] & if yes then why?

Answer 6

See, that is why it is called principal argument

Answer 7

but i have a book which says that \[\theta+2pi n\] are the values of the arguments but when theta lies between \[-pi \le \theta \le pi\] it is called its principle value .What does this mean?

Answer 8

I just wrote the same thing above

Answer 9

k! thanx a lot dude .I could't understand what u said earlier but now it is :)