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The Complex Numbers Z1 Z2 And Z3 Satisfying The Vertices Of A Triangle Which Is

Solution: Given (z1-z3)/(z2-z3) = (1-i√3)/2 (z2-z3)/(z1-z3) = (1+i√3)/2 (z2-z3)/(z1-z3) = cos π/3 + i sin π/3 |(z2-z3)/(z1-z3) | = 1 arg... View Article

Let Z Equal X Iy Be A Complex Number Whose X Y Are Integers

Solution: Given Put z = x+iy (x+iy)(x-iy)((x-iy)2+(x+iy)2 )= 350 (x2+y2)(2x2-2y2) = 350 (x2+y2)(x2-y2) = 175 = 25(7) x2+y2 = 25... View Article

For Complex Numbers Z1 Z2 If Z1 Eq 12 And Z2 3 Then Minimum Value Is

Solution: Given |z1| = 12 and |z2-3-4i| = 5 |z1-z2| ≥|z1| -|z2| |z2-3-4i| ≥ |z2| -|3+4i| |z2-3-4i| ≥ |z2| -√(32+42) |z2| ≥ 10 Minimum... View Article

If Xn Cos Pi By 2n Then X1 X2 X3 Infinity Equal

Solution: xn = cos (π/2n )+ i sin (π/2n) eiθ = cos θ+i sin θ Here θ = π/2n x1 = cos (π/2 )+ i sin (π/2) = ei(π/2) Similarly x2 =... View Article

Let Z Equal Cos Theta I Sin Theta Then The Value Of Sigma N 1 To 15

Solution: Given z = cos θ + i sin θ = eiθ = sin θ+ sin 3θ+sin 5θ+.....+sin 29θ = sin ((θ+29θ)/2 )sin ((15×2θ)/2 )/ sin (2θ)/2 = sin... View Article

If X 1 X Equal Root 3 Then X Equals

Solution: x +1/x = √3 x2+1 = √3x x2 -√3x+1 = 0 Roots = √3±√(3-4)/2 = (√3±√1)/2 = (√3±i)/2 (√3+i)/2 = cos π/6 + i sin π/6 Hence option... View Article

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