Argument of Complex Numbers formula:
A complex number can be written in polar form as the equation r(cosθ + i sinθ ), which serves as the argument in this particular case. Z represents the complex number, so arg(z) is the notation for the argument function. The complex number can be written as z = x + iy. The following formula can be used to perform the computation needed to analyse the complicated argument:
arg (z) = arg (x+iy) = tan-1(y/x)
As a result, the argument θ can be represented as follows:
Θ = tan-1 (y/x)
Properties of Argument of Complex Numbers:
Let’s take a look at some of the characteristics that are shared by the arguments of complex numbers. If we assume that z is a nonzero complex number and that n is any integer, then we can say that:
*arg(zn) = n arg(z)
Let us assume that z1 and z2 are two different complex numbers, then
1. arg (z₁/ z₂) = arg ( z₁) – arg ( z₂)
2. arg ( z₁ z₂) = arg ( z₁) + arg ( z₂)
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