The complex number [2[cos(π/10)+isin(π/10)]]^5 can be written as a+bi. What is the value of a+b?

Answer 1

by De Moivre's theorem

(2( cos (π/10 + i sin (π/10) )^5

= 2^5(cos (π/2) + i sin π/2)
= 32( 0 + i(1) )
= 0 + 32i

so a = 0 , b=32
a+b = 32