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If W Z Z 1 By 3 I And W 1 Then Z Lies On

Solution: Given w = z/(z-⅓)i and |w| = 1 w = 3z/(3z-i) |w| = 3|z|/|(3z-i)| 3|z| = |(3z-i)| Put z = x+iy |3(x+iy)| = |(3x+i(3y-1)|... View Article

Let Zw Be Two Complex Numbers Such That Bar Z I Bar W 0 And Arg Zw Pi Then Arg Z Equal

Solution: z = iw w = -iz arg (zw) = π arg (iz2) = π arg (-i)+2 arg(z) = π -(π/2) + 2 arg(z) = π Since arg (-i) = -(π/2) arg(z) =... View Article

If Z X Iy And Z 1 By 3 P Plus Iq Then X P Plus Y Q By P 2 Q2 Equal

Solution: Given z = x-iy and z1/3 = p+iq x-iy = (p+iq)3 x-iy = p3-3pq2+i(3p2q-q3) Equating real and imaginary part x = p3-3pq2 x/p =... View Article

If 1 Plus I X 2i By 3 I Plus 2 3i Y Plus I By 3 I I Then X Y Equal

Solution: Given ((1+i)x-2i)/(3+i) +((2-3i)y+i)/(3-i) = i [((1+i)x-2i)(3-i)/(3+i)(3-i)]+ [((2-3i)y+i)(3+i)/(3-i)(3+i)] = i... View Article

The Expression Of Complex Number 1 1 Cos Theta I Sin Theta In The Form A Plus Ib Is

Solution: 1/(1+cos θ-i sin θ) = 1(1+cos θ+i sin θ)/(1+cos θ-i sin θ) (1+cos θ+i sin θ) = (1+cos θ+i sin θ)/(1+cos θ)2+sin2θ = (1+cos θ+i sin... View Article

If The Cube Roots Of Unity Are 1 Omega Omega Square Then 1 Omega Omega2 Equal

Solution: We know sum of three cube roots of unity equals zero. 1+ω+ω2 = 0 (1+-½-√3i/2 + -½+√3i/2 = 0) Hence option (2) is the answer.... View Article

If Z Equal 4 3i 5 3i Then Z 1 Equal

Solution: Z = (4+3i)/(5-3i) Z-1 = 1/Z = (5-3i)/(4+3i) Multiply numerator and denominator with (4-3i) = (5-3i)(4-3i)/(4+3i)(4-3i) =... View Article

I Power 1 I Power 2 Plus Equal

Solution: i1+i2+i3+i4+...+i100 i1+i2+i3+i4= i-1+i+1 = 0 Powers of i follow a cyclicity of 4. So i1+i2+i3+i4+...+i100 = 0 Hence option... View Article

The Complex Numbers Z1 Z2 And Z3 Satisfying Z1 Z3 Z2 Z3 1 Root 3 I 2 Are The Vertices Of A Triangle Which Is

Solution: (z1-z3)/(z2-z3) = (1- √3i)/2 Multiply numerator and denominator with (1+√3i) = (1- √3i)(1+√3i)/2(1+√3i) = 1+1(3)/(2(1+√3i) =... View Article

Evaluate I Power 19 1 I Power 25 2

Solution: (i19+(1/i)25)2 = (i16 i3+1/i24 i)2 (since i4 = 1, i2 = -1) = ( -i+1/ i)2 = (-i+i3)2 = (-i-i)2 = (-2i)2 = 4 (-1) =... View Article

If Z X Iy X Y Belongs To R And 3x 3x Yi 4 6i Then Z

Solution: 3x+(3x-y)i = 4-6i Equate real part, we get 3x = 4 x = 4/3 Equate imaginary part, we get 3x-y = -6 3(4/3)-y = -6 4-y = -6 y =... View Article

Let Z And Omega Be Two Non Zero Complex Numbers Such That Z Omega And Arg Z Arg Omega Pi Then Z Equals

Solution: z = | z |(cos θ+ i sin θ) Where θ = arg z If θ1 = arg ω So θ = π- θ1 z = | ω | (cos (π- θ1)+ i sin (π- θ1 ) = | ω | (-cos θ1... View Article

If Z Not Equal 1 And Z 2 Z 1 Is Real Then The Point Represented By The Complex Number Z Lies

Solution: Let z = x+iy z2/(z - 1) = (x+iy)2/(x+iy-1) = (x2-y2+2xiy)/(x-1)+iy Multiply numerator and denominator with (x-1)-iy =... View Article

If Omega Equal E I2 Pi By 3 And A B C X Y Z Are Non Zero Complex Numbers Such That

Solution: Given ω = ei2π/3 |x|2+ |y|2+ |z|2= Also given a+b+c= x, a + bω + cω2 = y, a + bω2 + cω = z. Put the values of x, y and z... View Article

If Omega Is An Imaginary Cube Root Of Unity Then 1 Plus Omega Omega Square Power 7 Equals

Solution: (1 + ω − ω2)7 = (-ω2- ω2)7 = (-2ω2)7 = -128ω14 = -128ω2 Hence option (4) is the answer.... View Article

Which Is Non Magnetic Material

Which is non-magnetic material? Non-magnetic materials do not get attracted to a magnet. Examples of non-magnetic material are wood, plastic,... View Article

What Is Free Vibration And Forced Vibration

What is free vibration and forced vibration? In free vibration, energy will remain the same. Energy is not added or removed from the body. The... View Article

What Did Kepler Prove

What did Kepler prove? Kepler proposed the three laws of planetary motion. In Kepler’s first law he proved that the planets moved in an... View Article

How Can A Pendulum Be Used To Measure Gravity

How can a pendulum be used to measure gravity? The simple pendulum can be used to determine the time period using the formula From the... View Article

Is Activation Energy Dependent On Temperature

Is activation energy dependent on temperature? When there is an increase in temperature molecules start moving faster because they gain energy.... View Article

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