Which of the following is a solution to the equation z3 = (1 + √3i)

Question

Which of the following is a solution to the equation z3 = (1 + √3i) ?

(A) 21/3[cos(23π/18) + i sin(23π/18)] (B) 21/3[cos(8π/9) + i sin(8π/9)] (C) 21/3[cos(17π/18) + i sin(17π/18) (D) 21/3[cos(10π/9) + i sin(10π/9)] (E) 21/3[cos(13π/18) + i sin(13π/18)] (F) 21/3[cos(7π/9) + i sin(7π/9)] (G) 21/3[cos(11π/9) + i sin(11π/9)] (H) 21/3[cos(19π/18) + i sin(19π/18)]

Answer 1

z³=1 + √3 i=2e^iπ/3 = 2[cos(π/3)+isin(π/3)]

z=2^1/3e^iπ/9=2^1/3[cos(π/9)+i sin(π/9)]

Compare with answers above

 

 

(2 Exp[I \[Pi]/3])^(1/3)