(adsbygoogle = window.adsbygoogle || []).push({}); complex analysis-- Oscillation/vibration class

Hello all,

I'm taking a wave/vibration/oscillation class, and we're delving into complex notation for these.

One of our assigments dealt with a complex function that we didn't get a whole lot of practice out of in math methods.

I've gone back through my Boas' Math Methods text, as well as the Gradshtein Tables, and Zwillinger CRC Math tables book, and do not get very much from them in regards to solving these types of problems.

So-- perhaps someone with more skill than I can 'splain it to me.....

I get

Cos (w*t) + i* sin(w*t) = e^(i*w*t)

But the real to complex domain conversion still confuses me.

E.g. A^3=-1.

Maple 10 states that A = -1, .5+/- sqrt(3)*i/2 as the three solutions for this.

In trying to do the real to imaginary domain graph, as in the complex section of Boas' text, we have the typical x,y graph. Where the y becomes the imaginary plane.

If I do -1 as my point, it leaves me on the x axis, and no where in the imaginary plane.

However, it would appear that I should be somewhere off axis, and at .5 in the real space, and +/- sqrt(3)*i/2 in the imaginary plane.

anyone have a really good, comprehensive explanation to help stop my head-banging?

your assistance would be deeply appreciated.

Best,

SteveB.

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# Complex analysis- Oscillation/vibration class

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