Time remaining:
math college calculus

Mathematics
Tutor: None Selected Time limit: 1 Day

find all the complex fifth roots of −27 hint; z1/n= r1/n cos(θ+2πk/n )+i sin(θ+2πk/n )

Apr 2nd, 2015

  –27 = 27(cos π + i sin π) has five fifth roots

(–27)1/5 = 271/5 ({cos [π/5 + (2 /5)πk] + i sin [π/5 + (2 /5)πk]} where k = 0, 1, 2, 3, and 4

z1 = 271/5 [cos (π/5) + i sin (π/5)] = 1.56 + 1.14i

z2 = 271/5 [cos (3π/5) + i sin (3π/5)] =–0.597 + 1.84i

z3 = 271/5 [cos π + i sin π] = – 271/5 = – 1.93

z4 = 271/5 [cos (7π/5) + i sin (7π/5)] = – 0.597 – 1.84i

z5 = 271/5 [cos (9π/5) + i sin (9π/5)] = 1.56 – 1.14i

Apr 2nd, 2015

Are you studying on the go? Check out our FREE app and post questions on the fly!
Download on the
App Store
...
Apr 2nd, 2015
...
Apr 2nd, 2015
Dec 11th, 2016
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer