If X Equal Alpha Plus Beta Y Equal Alpha Omega Plus Beta Omega 2 Z Alpha Omega 2 Beta Omega Omega Is An Imaginary Cube Root Of Unity Then The Value Of Xyz Is
Given x = α + β, y = αω + βω2, z = aω2 +βω xyz = (α + β)(αω... View Article
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If 1 Omega And Omega 2 Are The Cube Roots Of Unity Then Omega 1 Omega 3 1 Omega 2 Is Equal To
ω(1+ ω)3– (1+ω)2 = ω((-ω2)3-(-ω2)2) = ω(-1-ω) = ωω2 = ω3 = 1 Hence option (1) is the answer.
If Z Equal 7 I By 3 4i Then Z Power 14 Is Equal To
Given z = (7-i)/(3-4i) Multiply numerator and denominator with (3+4i) (7-i)(3+4i)/(3-4i)(3+4i) = (21-3i+28i+4)/(9+16) = (25+25i)/25 = 1+i z14 = (1+i)14... View Article
The Minimum Value Of A B Omega C Omega 2 Where A B And C Are All Not Equal Integers And Omega Not Equal 1 Is A Cube Root Of Unity Is
We know 1+ω+ω2= 0 So ω2 = -(1+ω) |a + bω + cω2| = |a+bω +c(-(1+ω )) | = |(a-c)+(b-c)... View Article
If Omega Equal 1 Plus Root 3i By 2 Then 3 Plus Omega 3 Omega 2 4 Is
(3+ω+3ω2)4 = (2+1+ω+ω2+2ω2)4 = (2+0+2ω2)4 = [2(1+ω2)]4 = [2(-ω)]4 = 24 ω = 16ω Hence option (3) is the answer.
If Omega Is An Imaginary Cube Root Of Unity Then 1 Omega Omega 2 Power 7 Equals
Use ω3 = 1 and 1+ω = -ω2 (1+ ω – ω2)7 = (-ω2-ω2)7 = (-2ω2)7 = -27ω14 = -128... View Article
1 Plus Root 3 By 2 Power 100 1 Root 3 By 2 Power 100 Is Equal To
Let ω = (-1-√3i)/2 and ω2 = (-1+√3i)/2 ((-1+√-3)/2)100 +(-1-√-3)/2)100 = ((-1+√3i)/2)100 +(-1-√3i)/2)100 = (ω2)100+ω100 = ω200+ω100 = ω198ω2+ω99ω =... View Article
If I Equal Root 1 Then 4 Plus 5 1 By 2 Plus I Root 3 By 2 334 Is Equal
We know ω = (-½)+(√3/2) i 4+5(-½ +i√3/2)334+3(-½ +i√3/2)365 = 4+5ω334+3ω365 = 4+5(ω3)111+3(ω3)121ω2 = 4+5ω+3ω2 (since ω3 = 1) =... View Article
If I Z4 1 Equal 0 Then Z Can Take The Value
Given iz4 + 1 = 0 iz4 = -1 z4 = -1/i = i2/i = i = 0+i z= i1/4... View Article
If 1 A1 A2 An 1 Are The Nth Roots Of Unity Then The Value Of
Given1, a1, a2,…an-1 are the nth roots of unity. So xn-1= (x-1)(x-a1)…(x-an-1) ( xn-1)/(x-1) = (x-a1)(x-a2)…(x-an-1) xn-1+xn-2+…x2+x+1 = (x-a1)(x-a2)…(x-an-1) Substitute... View Article
If 1 Omega And Omega 2 Are The Cube Roots Of Unity Then 1 Up To 2n Factors Is
Use 1+ω = -ω2 and 1+ω2 = -ω (1 – ω + ω2) = -2ω (1 – ω2 + ω4)... View Article
A Value Of N Such That Root 3 By 2 Plus I By 2 N Equal 1 Is
Given (√3/2 +i/2)n = 1 => (cos θ+i sin θ)n = 1 => cos θ = √3/2 sin θ =... View Article
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Why are pole pieces of galvanometer made concave? The pole pieces of the galvanometer are made concave so that the... View Article
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