Its principal value $\DeclareMathOperator{\Arg}{Arg}\Arg(z)$ is real-valued and is defined on the set $$\mathbb C^{-\cdot}:=\mathbb C\setminus \{z = x + iy \mid x\leq 0,\, y=0 \}.$$ The principal value $\Arg(z)$ is the representive of $\arg(z)$ lying in the interval $\, ]-\pi,\pi[\,$, and can be expressed in terms of the $\arctan$ function
Worked Examples. Example 1. Find the modulus and argument of the complex number z = 3+2i z = 3 + 2 i. Solution. |z| = √32+22 = √9 +4 = √13 | z | = 3 2 + 2 2 = 9 + 4 = 13. As the complex number lies in the first quadrant of the Argand diagram, we can use arctan 2 3 arctan 2 3 without modification to find the argument.
An online calculator to calculate the modulus and argument of a complex number in standard form. Let Z Z be a complex number given in standard form by. Z = a + i Z = a + i. The modulus |Z| | Z | of the complex number Z Z is given by. |Z| = a2 + b2− −−−−−√ | Z | = a 2 + b 2.
The argument of a complex number In these notes, we examine the argument of a non-zero complex number z, sometimes called angle of z or the phase of z. Following eq. (4.1) on p. 49 of Boas, we write: z = x+iy = r(cosθ +isinθ) = reiθ, (1) where x = Re z and y = Im z are real numbers. The argument of z is denoted by θ, which is measured in
the complex number, z. The modulus and argument are fairly simple to calculate using trigonometry. Example.Find the modulus and argument of z =4+3i. Solution.The complex number z = 4+3i is shown in Figure 2. It has been represented by the point Q which has coordinates (4,3). The modulus of z is the length of the line OQ which we can find using
1. It is undefined. An easy way to see that it would be difficult to define it uniquely is to consider that the argument of a product is the sum of arguments, i.e: arg(z1z2) = arg(z1) + arg(z2) arg ( z 1 z 2) = arg ( z 1) + arg ( z 2) If we consider z1 = 0 z 1 = 0, we find: arg(0) = arg(0) + arg(z2) arg ( 0) = arg ( 0) + arg ( z 2) So therefore
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what is arg z of complex number
