Use this formula to find all the solutions of the equation? #x^3# + 8 =0 Trigonometry Trigonometric Identities and Equations Solving Trigonometric Equations 1 Answer Cesareo R. Dec 3, 2016 See below. Explanation: Using de Moivre's identity #e^(i phi) = cosphi + i sin phi# #x^3= -8 = -2^3=2^3e^(i(pi+2kpi))# for #k=0,1,2# then #x = 2 e^(i(pi+2kpi)/3)# so the roots are: #2 e^(ipi/3), 2 e^(ipi),2 e^(i(5pi)/3)# or #1 + i sqrt[3], -2, 1 - i sqrt[3]# Answer link Related questions How do you find all solutions trigonometric equations? How do you express trigonometric expressions in simplest form? How do you solve trigonometric equations by factoring? How do you solve trigonometric equations by the quadratic formula? How do you use the fundamental identities to solve trigonometric equations? What are other methods for solving equations that can be adapted to solving trigonometric equations? How do you solve #\sin^2 x - 2 \sin x - 3 = 0# over the interval #[0,2pi]#? How do you find all the solutions for #2 \sin^2 \frac{x}{4}-3 \cos \frac{x}{4} = 0# over the... How do you solve #\cos^2 x = \frac{1}{16} # over the interval #[0,2pi]#? How do you solve for x in #3sin2x=cos2x# for the interval #0 ≤ x < 2π# See all questions in Solving Trigonometric Equations Impact of this question 4498 views around the world You can reuse this answer Creative Commons License