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What's the quickest way to calculate the argument of $\displaystyle \pi e^{-\frac{3i\pi}{2}}$?
The argument of $\displaystyle \pi e^{-\frac{3i\pi}{2}}$ can take any value of the form $-\dfrac{3\pi}2 + 2k\pi$, where $k$ is an integer. If you want the principal value of the argument then you need to choose $k$ so as to get a value in the range $(-\pi,\pi]$ (or maybe $[0,2\pi)$, depending on which definition you are using for the principal range). In this example, you would want $k = 1$, giving the principal value of the argument as $\dfrac\pi2.$Guest said:What's the quickest way to calculate the argument of $\displaystyle \pi e^{-\frac{3i\pi}{2}}$?
Thank you very much! :DOpalg said:...
The argument of a complex number is the measure of the angle between the positive real axis and the vector representing the complex number in the complex plane.
Calculating the argument of a complex number is important in understanding the properties and behavior of complex numbers, as well as in solving problems in various fields such as physics, engineering, and mathematics.
The quickest way to calculate the argument of a complex number is by using the inverse tangent function (arctan) of the imaginary part divided by the real part of the complex number. This can be represented as arg(z) = arctan(Im(z)/Re(z)).
Yes, there are other methods such as using the polar form of a complex number (z = r(cos θ + i sin θ)), where the argument is represented by θ. Another method is using the properties of complex numbers, such as the conjugate property, to calculate the argument.
Yes, the argument of a complex number can be negative. It can take on any value between -π and π, depending on the position of the complex number in the complex plane. A negative argument indicates that the vector representing the complex number is in the lower half of the complex plane.