Question
Use De Moivre's Theorem to write the complex number in trigonometric form
(cos(2pi)/7)+ i sin((2pi)/7))^5
(cos(2pi)/7)+ i sin((2pi)/7))^5
Answers
Reiny
(cos(2pi)/7)+ i sin((2pi)/7))^5
= 1^5(cos (10π/7) + i sin(10π/7)
= (cos (-4π/7) + i sin(-4π/7) , after subtracting 2π from the angle
= (cos (4π/7) - i sin(4π/7) )
= 1^5(cos (10π/7) + i sin(10π/7)
= (cos (-4π/7) + i sin(-4π/7) , after subtracting 2π from the angle
= (cos (4π/7) - i sin(4π/7) )