1. find the root of the equation Z^2 - Z + 1 =0
^ means to the power of.
2007-09-04 04:08:52 · 4 answers · asked by Mystic healer 4 in Science & Mathematics ➔ Mathematics
Z = [ 1 ± √ (1 - 4) ] / 2
Z = [ 1 ± √ ( - 3 ) ] / 2
Z = [ 1 ± i √3 ] / 2
2007-09-07 21:23:32 · answer #1 · answered by Como 7 · 0⤊ 0⤋
z^2 -z +1 = 0
roots are (+or –) 1/2 + sq.root (1 – 4)/2
z = + [1/2 + sq.root (1 – 4)/2]
= + [1/2 + (sq.rt. 3) i/2] -----------where i = sq.rt. of – 1
or
z = – [1/2 + sq.root (1 – 4)/2]
= = – [1/2 + (sq.rt. 3) i/2]
2007-09-06 11:41:45 · answer #2 · answered by Pranil 7 · 0⤊ 0⤋
z = 1/2[1 + Sqrt (-3)] or 1/2[1 - Sqrt (-3)]
z = 1/2[1 + i Sqrt (3)] or 1/2[1 - i Sqrt (3)]
where i = Sqrt(-1)
2007-09-04 11:35:05 · answer #3 · answered by cllau74 4 · 0⤊ 0⤋
z^2 -z +1 = 0
z = [ 1+-sqr(1-4) ] /2
z = 1/2 + sqr(3) i
z = 1/2 - sqr(3) i
2007-09-04 11:19:12 · answer #4 · answered by CPUcate 6 · 0⤊ 0⤋