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The Amplitude Of E Power E I Theta Is Equal To

Solution: ecos θ-i sin θ = ecos θ e -i sin θ = ecos θ|e -i sin θ| = ecos... View Article

Real Part Of E Ei Theta Is

(1) ecos θ( cos (sin θ) (2) ecos θ( cos (cos θ) (3) esin θ( sin (cos θ) (4) esin... View Article

If 1 I Root 3 9 A Ib Then B Is Equal To

Solution: (1+i√3)9 = a+ib = 29 [(½)+(√3/2)i ]9 = 29 [ cos π/3 + i sin π/3]9 Apply de moivre’s... View Article

The Value Of I 1 By 3 Is

Solution: Let x3 = -i x3+i = 0 (x3-(i)3 )= 0 (x-i)(x2-1+ix) = 0 x – i = 0 or... View Article

If Y Cos Theta I Sin Theta Then The Value Of Y 1 Y Is

Solution: Given y = cos θ+i sin θ 1/y = 1/(cos θ+i sin θ) Multiply numerator and denominator with (cos... View Article

If 1 Root 3 R Ei Theta Then Theta Is Equal

Solution: Given -1+√-3 = reiθ -1+√-3 = -1+√3i -1+√3i = r(cos θ+i sin θ) r cos θ = -1 r... View Article

If Z R Ei Then E Iz Is Equal To

(1) er sin θ (2) e-r sin θ (3) e-r cos θ (4) er cos θ Solution: Given z =... View Article

1 7i 2 I 2 Is Equal To

(1) √2 [cos (3π/4)+i sin (3π/4)] (2) √2 [cos (π/4)+i sin (π/4)] (3) cos (3π/4)+i sin (3π/4) (4) None of... View Article

If Root A Ib X Iy Then Possible Value Of Root A Ib Is

Solution: √(a+ib) = x+iy Squaring both sides (a+ib) = (x+iy)2 = x2-y2+2ixy Comparing real and imaginary parts a = x2-y2... View Article

If Ei Theta Cos Theta I Sin Theta Then In Triangle Abc Value Of

Solution: Given eiθ = cos θ+ i sin θ In triangle A+B+C = 1800 = π eiA.eiB.eiC = ei(A+B+C) =... View Article

If X Iy Root A Ib C Id Then X2 Y2 2 Is Equal To

(1) (a2+b2)/(c2+d2) (2) (a+b)/(c+d) (3) (c2+d2)/(a2+b2) (4) [(a2+b2)/(c2+d2)]2 Solution: Given x+iy = √[(a+ib)/(c+id)] ..(i) x-y = √[(a-ib)/(c-id)] …(ii) Multiply (i)... View Article

If 7 24i 1 2 X Iy Then X2 Y2 Is Equal To

Solution: (-7-24i)1/2 = x-iy Squaring both sides (-7-24i) = (x-iy)2 (-7-24i) = x2-2xyi-y2 Equating real and imaginary part x2-y2 =... View Article

If Z Is Any Complex Number Satisfying Z 3 2i Less Than Or Equal 2 Then The Value Of

Solution: We know |z1|- |z2| ≤|z1+z2| ≤|z1|+|z2| Given |z-3-2i| ≤ 2 |2z-6+5i| = 2|z-3+(5/2)i| = 2|z-3-2i+(9/4)i| = |2-9/4| = 5/2... View Article

The Value Of The Sum Sigma N 1 To 13 I N I N 1 Where I Root 1 Equals

Solution: ∑n=113 (in+in+1) = ∑n=113 in(1+i) = (1+i) ∑n=113 in = (1+i)(1+i2+i3+…i13) = (1+i)(i(1-i)/(1-i)) = (1+i)i = -1+i = i-1... View Article

The Number Of Points In Infinity For Which X2 X Sin X Cos X 0 Is

Solution: Given f(x) = x2-x sin x- cos x = 0 f’(x) = 2x-x cos x-sinx+sinx = 2x-x cos x... View Article

Let Z1 And Z2 Be Two Complex Numbers With Alpha And Beta As Their Principal Arguments Such That Alpha Plus Beta Greater Pi

Solution: arg z1 = α arg z2 = β α + β > π -π < arg z ≤ π... View Article

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