If Z2 Z 1 0 Where Z Is A Complex Number Then The Value Of Z 1
Given z2 + z + 1= 0 z = ω, ω2 (z+1/z)2 +(z2+1/z2)2 +(z3+1/z3)2 +….+(z6+1/z6)2 = = (ω+ω2)2+(ω+ω2)2+(ω3+1/ω3)2+(ω+ω2)2+(ω+ω2)2+(ω6+1/ω6)2 = 4(ω+ω2)2+2(ω3+1/ω3)2... View Article
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The Expression Sin X 2 Cos X2 I Tan X 1 2isinx 2 Is Real Then The Set Of All Possible Values Of X Is
[sin (x/2)+cos (x/2)-i tan (x)]/[(1+2isin(x/2)] Multiply numerator and denominator (1-2i sin (x/2)) Since it’s real, equate the imaginary part to... View Article
If N Is A Positive Integer Then 1 Plus I Root 3 N Plus 1 I Root3 N Is Equal To
(1+√3i) = 2 cos π/3 + i sin π/3 (1-√3i) = 2 cos π/3 – i sin π/3 (1+ i√3)n... View Article
If Alpha Is A Complex Number Satisfying The Equation Alpha 2 Alpha Plus 1 Equal 0 Then Alpha 31 Is Equal To
x3 = 1 (cube root of unity) x3-1 = 0 (x-1)(x2+x+1) = 0 x = 1 or (x2+x+1) = 0... View Article
If Omega Not Equal 1 Is A Cube Root Of Unity Then The Sum Of The Series S 1 Is
S = 1+ 2ω+ 3ω2 + • • • + 3ω3n-1 Multiply by ω Sω =ω+ 2ω2+ 3ω3 + •... View Article
If 3 By 2 Plus I Root3 By 2 Power 50 Equal 3 25 X Iy Where X And Y Are Real Then The Ordered Pair X Y Is
Given [(3/2)+i(√3/2)]50 = 325(x+iy) [(√3/2)+i/2]50 = x+iy i50 [ (-1+i√3)/2]50 = x+iy I50ω50 = x+iy = i2ω2 = -ω2 =>... View Article
If The Fourth Roots Of Unity Are Z1 Z2 Z3 And Z4 Then Z1 Z2 Z32 Z42 Is Equal To
If z is the fourth root of unity, z4 = 1 (z4-1) = 0 (z2-1)(z2+1) = 0 z = 1,-1,i,-i... View Article
The Value Of 1 Plus Root3i 4 Plus 1 Root 3i4 Is
If z = r ( cos θ+i sin θ), then zn = rn(cos nθ+i sin nθ) (1+√3i) = 2(cos π/3... View Article
If Root 3i Plus 1 Power 100 Equal 2 99 A Plus Ib Then A2 B2 Is Equal To
Given (√3i + 1)100 =299 (a + ib) ω = (-1+i√3)/3 = (i2+i√3)/2 √3+i = 2ω/i = -2ωi (√3+i )100... View Article
The Modulus And Amplitude Of 1 Plus 2i By 1 1 I Square Are
(1+2i)/(1-(1-i)2 = (1+2i)/(1-(1-2i-1) = (1+2i)/(1+2i) = 1 = ei0 Modulus is 1 and amplitude is 0. Hence option (2) is... View Article
If A Equal Z 1 Z Plus 1 Is Purely Imaginary Number
Let z = x+iy (z-1)/(z+1) = (x+iy-1)/(x+iy+1), z ≠-1 = (x-1+iy)/(x+1+iy) = (x-1+iy)(x+1-iy)/(x+1+iy)(x+1-iy) = (x2-1)+y2+i[(x+1)-y(x-1)]/((x+1)2+y2) Given (z-1)/(z+1) is a purely... View Article
The Number Of Non Zero Integral Solutions Of The Equation 1 Ix 2x Is
|1 – i|x = 2x (√2)x = 2x 2x/2 = 2x 2x/2 = 1 2x/2 = 20 x/2 = 0... View Article
The Magnitude And Amplitude Of 1 I 3 2 2i 3 I Are Respectively
(1+i√3)(2+2i)/(√3-i) Multiply numerator and denominator with (√3+i) (1+i√3)(2+2i)(√3+i)/(√3-i)(√3+i) = 2(i+1)(√3+3i+i-√3)/4 = 2(-1+i) = -2+2i Magnitude = √(22+22) = √8 =... View Article
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The transfer of heat through electromagnetic energy is known as radiation. The heat that we feel when we stand next... View Article
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No, we don’t prefer to use a Zener Diode in a rectifier circuit because for a rectifier circuit a high... View Article
How Do Sound Waves Travel
Sound waves are produced by a source such as the vibrating diaphragm of stereo speakers. The sound source creates vibrations... View Article
How Do You Find Youngs Modulus From A Load Extension Graph
Young’s modulus sometimes referred to as modulus of elasticity measures the ability of the material to withstand changes in length... View Article
Is Light A Particle
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Does Pressure Affect Buoyancy
The buoyant force is the upward force of the rising water exerted upon the object by the fluid. The fluid... View Article
How Do You Know If A Resistor Is In Parallel
The nodes in the circuit help us determine if the connected resistors are in series or parallel. A node in... View Article
