Hi all! Once again stuck on complex numbers...
(a) Expand (c+is)^4, where i^2 = -1. Hence by using De Moivre's theorem, show that
sin4@/cos4@ = (4c^3s - 4cs^3)/ (c^4 - 6c^2s^2 + s^4), where c = cos@, and s = sin @
I expanded to get c^4 + 4c^3si - 6c^2s^2 - 6cs^3i + s^4, and I see that sin4@/cos4@ is just s^4/c^4. But not sure how to show the solution.
(b) By substituting t = s/c = tan@, deduce an expression for tan4@ in terms of t only. Hence show that tan4@ = 0, when 4t - 4t^3 = 0
(c) Solve the equation obtained in part b for t. Hence find the values of @ in the range -pie/2 less than @ less than pie/2, for which tan4@ = 0.
Thanks once again for the help!