answersLogoWhite

0


Best Answer

A complex number (z = x + iy) can be plotted the x-y plane if we consider the complex number the point (x,y) (where x is the real part, and y is the imaginary part). So once you plot the complex number on the x-y plane, draw a line from the point to the origin. The Principle Argument of z (denoted by Arg z) is the measure of the angle from the x-axis to the line (made from connecting the point to (0,0)) in the interval (-pi, pi]. The difference between the arg z and Arg z is that arg z is an countably infinite set. And the Arg z is an element of arg z. Why? : The principle argument is needed to change a complex number in to polar representation. Polar representation makes multiplication of complex numbers very easy. z^2 is pretty simple: just multiply out (x+iy)(x+iy). But what about z^100? This is were polar represenation helps us, and to get into this representation we need the principle argument. I hope that helped.

User Avatar

Wiki User

โˆ™ 2009-01-23 23:40:23
This answer is:
User Avatar
Study guides

Algebra

20 cards

A polynomial of degree zero is a constant term

The grouping method of factoring can still be used when only some of the terms share a common factor A True B False

The sum or difference of p and q is the of the x-term in the trinomial

A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

โžก๏ธ
See all cards
3.8
โ˜†โ˜…โ˜†โ˜…โ˜†โ˜…โ˜†โ˜…โ˜†โ˜…
1785 Reviews

Add your answer:

Earn +20 pts
Q: Why and what is principle argument of complex number?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Continue Learning about Other Math

Definition of principle square root?

The square root of a positive real number can either be +/-. The principle square root is defined as the positive value. sqrt(9) is +/- 3, but the principle square root of 9 is 3. For complex numbers the principle square root is the argument (or angle) of the complex number that lies between (-pi,pi]. I am pretty sure that the upper angle pi is closed while the lower angle -pi is open, but not 100%.


Why you restrict the argument of a complex number between -pi and pi?

Because the trigonometric functions (sine and cosine) are periodic, with period 2*pi. If the argument were not restricted, you would have an infinite number of answers. You could, of course, restrict the argument to any interval of size 2*pi: 3.5pi to 5.5pi, for example.


Adjoint operator of a complex number?

Adjoint operator of a complex number?


Is 3i an irrational number?

The imaginary part of the complex number โ€“5 + 3i is


Is every real number a complex number?

A complex number is a number of the form a + bi, where a and b are real numbers and i is the principal square root of -1. In the special case where b=0, a+0i=a. Hence every real number is also a complex number. And in the special case where a=0, we call those numbers pure imaginary numbers. Note that 0=0+0i, therefore 0 is both a real number and a pure imaginary number. Do not confuse the complex numbers with the pure imaginary numbers. Every real number is a complex number and every pure imaginary number is a complex number also.

Related questions

Definition of principle square root?

The square root of a positive real number can either be +/-. The principle square root is defined as the positive value. sqrt(9) is +/- 3, but the principle square root of 9 is 3. For complex numbers the principle square root is the argument (or angle) of the complex number that lies between (-pi,pi]. I am pretty sure that the upper angle pi is closed while the lower angle -pi is open, but not 100%.


What is the difference between principal argument and argument of a complex number?

PRINCIPAL ARGUMENT = ARGUMENT + 2nPI arg(Z) = Arg (Z) + 2nPI


The (blank) of a complex number z=r(cos(theta) + i * sin(theta)) is the angle theta?

Argument Hopes this help!!


How do you find square root of a complex number?

This is best done if the complex number is in polar coordinates - that is, a distance from the origin, and an angle. Take the square root of the argument (the absolute value) of the complex number; and half the angle.


How do you find the argument of the complex number -2-i?

arg(-2-i) = sqrt[22 + 12] = sqrt(5)


True or false: When its argument is restricted to (0,2pi), the polar form of a complex number is not unique?

False apex


The structure of an argument can be somewhat complex The supported part of an argument is known as the?

conclusion


What is an essential ingredient of the Ricardo argument?

Answer this question Malthusian principle…


What is one general principle in the deductive argument of the declaration?

wap


Why you restrict the argument of a complex number between -pi and pi?

Because the trigonometric functions (sine and cosine) are periodic, with period 2*pi. If the argument were not restricted, you would have an infinite number of answers. You could, of course, restrict the argument to any interval of size 2*pi: 3.5pi to 5.5pi, for example.


What mathematical principle is equal to 3.14?

That's not a "mathematical principle", it is an approximation of the number pi.That's not a "mathematical principle", it is an approximation of the number pi.That's not a "mathematical principle", it is an approximation of the number pi.That's not a "mathematical principle", it is an approximation of the number pi.


What type of sentence is Tom and Jerry have a big argument every morning over what they should do with their day?

complex sentece

People also asked