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Restricting the argument of a complex number between -π and π is a common practice because it allows for a unique representation of the number in polar form. This range ensures that the principal argument lies within one full rotation in the complex plane, simplifying calculations involving angles and trigonometric functions. Additionally, it helps avoid ambiguity and ensures consistency in mathematical operations involving complex numbers.
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Lao
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JudyOh, dude, it's like when you're dealing with complex numbers, you gotta keep them in check, you know? So, by restricting the argument between -pi and pi, you're basically just making sure your complex number stays in line and doesn't go off causing trouble in the mathematical neighborhood. It's like giving them a curfew to prevent any wild imaginary escapades.
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Why and what is principle argument of complex number?
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.
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%.
Adjoint operator of a complex number?
Adjoint operator of a complex number?
Is 3i an irrational number?
No. It is an imaginary (or complex) number.
Find smallest positive divisor of an integers other then 1?
There is no such number. If you restrict yourself to integers, there are numbers - such as primes, that are not divisible by an integer other than one. And if you do not restrict yourself to intgers, then there is no smallest number sincce given any number, half that number will be smaller and will be a divisor.
