Any help with this would be greatly appreciated.
Solve the equation: x^5 + 1 = 0 . Give the 5 solutions in both trigonometric form and standard form.
2007-07-07 08:12:20 · 4 answers · asked by realpoeticyouth 1 in Science & Mathematics ➔ Mathematics
xxxxx + 1 = 0.
xxxxx = -1.
x = -1
x = -cos 0.
2007-07-07 08:23:11 · answer #1 · answered by Mark 6 · 0⤊ 0⤋
x^5=-1
x=(-1+0i)^(1/5)
=(cos (pi+k*360)+i sin (pi+k*360))^(1/5)
x_k=cos (36+k*72)+isin(36+k*72)
x_0=cos36+isin36
x_1=cos108+isin108
x_2=cos 180+isin180
x_3=cos (36+3*72)+isin(36+3*72)
x_4=cos(36+4*72)+isin(36+4*72)
try to simplify the roots.
2007-07-07 08:26:31 · answer #2 · answered by iyiogrenci 6 · 0⤊ 0⤋
x^5 = -1, or x =(-1)^(1/5)
x^5 = cos(pi+2.n.pi), or x = {Cos(pi + 2.n.pi)}^(1/5)
x^5 = cosA = {e^(iA) + e^(-iA) }/2,
or x=[{e^(iA) + e^(-iA) }/2]^(1/5)
x^5 = sqrt(1-sin^A) ...
2007-07-07 08:49:55 · answer #3 · answered by Snoopy 3 · 0⤊ 0⤋
tough one.
2007-07-07 08:19:27 · answer #4 · answered by Anonymous · 0⤊ 0⤋