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If Rooti5 3i Power 33 2 49z Then Modulus Of The Complex Number Is

Given (√5+√(3i))33 = 249z Take modulus |√5+√3i)33| = |249z| |√5+√3i)|33 = 249|z|... View Article

If Omega Is An Imaginary Cube Root Of Unity And X Equal A Plus B Y A Omega B Omega 2 Z A Omega2 B Omega Then X2 Y2 Z2 Is Equal To

Given ω is an imaginary cube root of unity x = a + b y = aω + bω2 z = aω2 + bω x2+y2+z2 =... View Article

If Omega Is A Complex Cube Root Of Unity Then Sin Omega 10 Omega 23 Pi By 4 Is Equal To

sin ω10+ω23π-π/4 = sin ω+ω2π-π/4 (Since ω is a cube root of unity) = sin -π-π/4 ( since... View Article

If Square Root Of 7 24i Is X Iy Then X Is Equal To

Let root of -7+24i = x+iy Squaring both sides (-7+24i ) = (x+iy)2 = x2-y2+2xiy Compare real and imaginary part x2-y2 = -7 2xy = 24 solving... View Article

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 = =... View Article

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... 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 + (1 - i√3)n = 2n(cos... 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 x not equal to 1 (x2+x+1) = 0 If α satisfies the... 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 =... 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 So z12+ z22+ z32+ z42 = 1+1+i2+i2 = 2-2 = 0 Hence... 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 + i sin π/3) (1+√3i)4 =... 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 the answer.... 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) =... 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 So x = 0 So the given equation has no non-zero integral solution.... 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)... View Article

How Is Heat Transferred By Radiation

The transfer of heat through electromagnetic energy is known as radiation. The heat that we feel when we stand next to a fire is the heat... View Article

Why Is Zener Diode Is Not Used In Rectifiers

No, we don’t prefer to use a Zener Diode in a rectifier circuit because for a rectifier circuit a high maximum peak inverse voltage is required.... 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 in the surrounding... View Article

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