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

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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.

Adjoint operator of a complex number?

The imaginary part of the complex number –5 + 3i is

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%.

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

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

Argument Hopes this help!!

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.

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

False apex

When a complex number is multiplied by its conjugate, the product is a real number and the imaginary number disappears.

Graphically, the conjugate of a complex number is its reflection on the real axis.

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.

yes

In the complex field, the two numbers are the same. If you restrict yourself to real solutions, the relationship is as follows: A polynomial of degree p has p-2k real solutions where k is an integer such that p-2k is non-negative. [There will be 2k pairs of complex conjugate roots.]

You can the number into the blacklists of your mobile phone.

If you add two complex numbers, the resulting complex number is equivalent to the vector resulting from adding the two vectors. If you multiply two complex numbers, the resulting complex number is equivalent to the vector resulting from the cross product of the two vectors.

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