Question

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. (Round terms to four decimal places.)?

[3(cos`pi/15`+ i sin `pi/15)]^7`

Answer 1

2187 `[cos ((7pi)/15) + i sin ((7pi)/15)]`

Explanation:

Direct application of De Moivre's theorem would give the result as `3^7 [cos ((7pi)/15) +isin ((7pi)/15) ]`

=2187 `[cos ((7pi)/15) + i sin ((7pi)/15)]`