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The Complex Number Z X Iy Which Satisfies The Equation Z 3i Z 3i 1 Lie On

If Z Is A Complex Such That Z Greater Than Or Equal To 2 Then The Minimum Value Of Z 1 2

Given |z| ≥ 2. It is the region on or outside the circle with center is (0,0) and radius 2. Minimum |z+1/2| is the distance of z which lie... View Article

If 1 Omega And Omega 2 Are The Cube Roots Of Unity 3 Omega 2 Omega 4 6 Is Equal To

(3 + ω2 +ω4)6 = (2+1+ω2 +ω3ω)6 = (2+1+ω2+ω)6 = 26 = 64 Hence option (1) is the answer.... View Article

Which Of The Following Is A Fourth Root Of 1 2 I Root 3 2

1/2 + i √3/2 = cos π/3+i sin π/3 = eiπ/3 = cis(π/3) Fourth root = eiπ/12 = cis(π/12) Hence option (1) is the answer.... View Article

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

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... View Article

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 =... 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

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... View Article

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... 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 =... 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 z = (cos π/2 + i sin π/2)¼ = cos π/8 + i sin π/8 Hence... 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... 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) = (1 - ω2 + ω3... 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 = ½ => θ = 300... View Article

Why Are Pole Pieces Of Galvanometer Made Concave

Why are pole pieces of galvanometer made concave? The pole pieces of the galvanometer are made concave so that the current-carrying coil and the... View Article

Why Ac Is Dangerous Than Dc

Why ac is dangerous than dc?. Alternating current (A.C) is five times more dangerous than Direct current (D.C). The frequency of the alternating... View Article

What Is The Principle Of Vernier Caliper

Vernier caliper is an amazing instrument used for measuring lengths. The reading on a vernier caliper is more accurate than a normal ruler. This... View Article

What Is The Function Of A Voltmeter

What is the function of a voltmeter? A voltmeter is an instrument used for measuring the voltage or potential difference between two points in an... View Article