What is the range of argument of complex number?

The argument 𝜃 of a complex number is, by convention, given in the range − 𝜋 < 𝜃 ≤ 𝜋 . However, we can also discuss a complex number with an argument greater than 𝜋 or less than − 𝜋 . The argument of a complex number within the range ] − 𝜋 , 𝜋 ] is called the principal argument.

Can argument of a complex number be zero?

The complex number has magnitude zero, but doesn’t really have an angle. The angle of a complex number is defined by where the ray through the origin and the complex number intersects the unit circle. So, the argument of zero is undefined.

What can be said about a complex number where a 0?

Notation. A real number a can be regarded as a complex number a + 0i, whose imaginary part is 0. A purely imaginary number bi is a complex number 0 + bi, whose real part is zero.

What is the difference between argument and principal argument of 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.

How do you find the argument and principal argument of a complex number?

In simple terms, by analysing the complex number, represented by point P(Re(z),Im(z)) in the argand plane, the principal argument can be defined as the angle that the line OP makes with the +ve x-axis. The value of principal argument is such that -π < θ =< π.

What is a complex argument?

An argument is complex if it contains a sub-argument, that is, if one of the premises for the main conclusion is also the conclusion for the other premise for the main argument. One premise of an argument is related to another premise in the argument in a premise/conclusion relationship.

Can the argument of a complex number be negative?

Negative Components When the real number is negative, the answer from the tangent operation must be adjusted. For example, when calculating the argument of the complex number -5 + 3i, the answer would be negative.

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 a principal argument of 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 does argument mean in complex number?

The argument of a complex number is defined as the angle inclined from the real axis in the direction of the complex number represented on the complex plane. It is denoted by “θ” or “φ”. It is measured in the standard unit called “radians”. In this diagram, the complex number is denoted by the point P.

What is the argument of non-zero complex numbers?

Under both definitions, it can be seen that the argument of any non-zero complex number has many possible values: firstly, as a geometrical angle, it is clear that whole circle rotations do not change the point, so angles differing by an integer multiple of 2π radians (a complete circle) are the same, as reflected by figure 2 on the right.

What is a complex number with zero imaginary part called?

Also, a complex number with zero imaginary part is known as a real number. The argument of a complex number is defined as the angle inclined from the real axis in the direction of the complex number represented on the complex plane. It is denoted by “θ” or “φ”. It is measured in the standard unit called “radians”.

What is the required value of complex argument for the given complex?

This value followed by the unit “radian” is the required value of complex argument for the given complex number. Find the argument of the complex number 2 + 2√3i. Let z = 2 + 2√3i.

What is the argument of zero in calculus?

The argument of zero is usually left undefined. Figure 3. The principal value Arg of the blue point at 1 + i is π/4. The red line here is the branch cut and corresponds to the two red lines in figure 4 seen vertically above each other). by circling the origin any number of times.