Write this expression in the standard form a + bi.

Question

Write this expression in the standard form a + bi.

 

(2(cos(pi/10)+isin(pi/10)))^5

Answer 1

By DeMoivre's Theorem, 

 

[2(cos(π/10) + isin(π/10))]⁵ = 2⁵[cos(5(π/10)) + i sin(5(π/10))]

 

                                                     = 32[cos(π/2) + i sin(π/2)]

 

                                                     = 32[0 + i(1)] = 32i