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Math - complex numbers

posted by on .

These questions are related to de moivre's theorem:

z^n + 1/z^n = 2cosntheta
z^n - 1/z^n = 2 isin ntheta

1. Express sin^5theta in the form Asintheta + Bsin3theta + Csin5theta and hence find the integral of sin^5theta.

2. Express sin^6theta in multiples of costheta and hence evaluate the integral of sin^6theta between 0 and pi/2.

3. Evaluate the integral of cos^7theta between pi/2 and 0.

The answers are:
1. -1/80cos5theta + 5/48cos3theta - 5/8costheta

2. 5pi/32

3. 5pi/32

Could you please guide me through the solutions, thank you SO much :)

  • Math - complex numbers - ,

    If you had posted one at I time, I could have helped with one of them. It is past my bedtime here.

    When you say "between pi/2 and 0" do you mean from pi/2 to zero? That would be backwards.

    Please be more specific.

  • Math - complex numbers - ,

    Sorry, yes I meant from 0 to pi/2 for the last two questions.

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