Studying Mathematics Thread

[Aliza]

In other words, if you multiply two expressions of the form cos(A)+i*sin(A), the result can be obtained by *adding* the angles involved.

Now, what happens if you multiply the *same* expression over and over again? The angle adds up again and again, however many times you did the multiplication.

That is why

[cos(A)+i*sin(A)]^n = cos(n A)+i*sin(n A)

Each multiplication corresponds to an addition of the angles.

So I took out paper and pencil and worked it out along with your example. I can clearly see how cosine and sine sum/difference formulas fit into DeMoivre's theorem. Sometimes I need it spelled out, but once I started following along with you, it was clear where the steps would take me. I was still scratching my head over how the exponent plays into this, but then it hit me like a ton of bricks. I see the little cycle there of adding and multiplying.

In short, you've effectively explained it to me, so thank you.