Table of Contents

## What is the principal value of the argument of a complex number?

The principal value is simply what we get when we adjust the argument, if necessary, to lie between -π and π. For example, z = 2e5 i/4 = 2e-3 i/4, subtracting 2π from the argument 5π/4, and the principal value of the argument of z is -3π/4.

**What is the difference between argument and principal argument in complex number?**

1. What is the difference between general argument and principal argument of a complex number? The value of the principal argument is such that -π < θ =< π. However, because θ is a periodic function having period of 2π, we can also represent the argument as (2nπ + θ), where n is the integer.

### Is argument and principal argument the same?

It’s not a matter of “principal argument” vs “argument”. If π/4 is an argument of a point, that is by definition the principal argument. For the argument to be π/4 your point must be in the first quadrant, but for tan(θ)=ℑ(z)/ℜ(z)=1 it could be in either first or third quadrant.

**What is the range of argument of a complex number?**

The argument of a complex number is the angle, in radians, between the positive real axis in an Argand diagram and the line segment between the origin and the complex number, measured counterclockwise. The argument 𝜃 of a complex number is, by convention, given in the range − 𝜋 < 𝜃 ≤ 𝜋 .

#### What is the principal value of the argument of a complex?

The “argument” of a complex number is just the angle it makes with the positive real axis. EXAMPLES: It seems silly not to keep the same convention for all quadrants but “officially” the principal value of the argument is – 180 < θ ≤ 180.

**What is the principal value of arg(z)?**

This special choice is called the principal value or the main branch of the argument and is written as Arg(z). Note that there is no general convention about the definition of the principal value, sometimes its values are supposed to be in the interval [0, 2π).

## What is the general argument of a complex number?

General argument of a complex number can be anything but the principal argument lies between. (-π, π] . If you express a complex number in polar coordinates, the angle isn’t unique, because sin and cos are periodic (with period of 2 * pi).

**What is the principal argument for Z = A + B I?**

−π < θ + 2π n ≤ π. Then, θ + 2π n is the principal argument. There is always one, and only one, value of n satisfying that constraint. When converting the Cartesian form of z = a + b i to polar form, n is normally 0.