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If A Equal Cos 2pi By 7 Plus I Sin 2pi By 7 Then The Quadratic Equation Whose Roots Are

(1) x2-x+2 (2) x2+x-2 (3) x2-x-2 (4) x2+x+2 Solution: a = cos 2π/7 + i sin 2π/7 ( so a7... View Article

If Z Iz And Z Plus Iz Are The Vertices Of A Triangle Whose Area Is 2 Units Then The Value Of Z Is

Solution: Let z = x+iy iz = -y+ix z+iz = (x+iy+i(x+iy) = (x-y)+i(x+y) So the vertices of the triangle are... View Article

If Z Equal X Plus Iy X Y Belongs To R And Mod X Plus Y Less Than Or Equal To Kz Then K Equal

Solution: z = x+iy (|x|-|y| )2 ≥0 |x|2+|y|2-2|x||y| ≥0 2|x||y| ≤ |x|2+|y|2 |x|2+|y|2+2 |x| |y|≤ 2 |x|2+2 |y|2 (|x|+|y|)2 ≤... View Article

If Z Is A Complex Number Satisfying Z I Re Z Z Imz Then Z Lies On

If W Is One Cube Root Of Unity Then Find The Determinant

Solution: Use w3 = 1 -1-w2 = w = = 1(w2-w4)-1(w-w2)+1(w2-w) = (w2-w)-w+w2+w2-w = 3w2-3w = 3w(w-1) Hence option (2)... View Article

Let Z Be Complex Number With Modulus 2 And Argument 2 Pi 3 Then Z Equal

Solution: Given modulus = 2 Argument is 2π/3. r = |z| = 2 x = r cos θ y =... View Article

If Given Determinant X Iy Then

Solution: Given = 6i(-3+3)+3i(4i+20)+1(12-60i) = 3i(20+4i)+12-60i = 60i-12+12-60i = 0+0i Comparing with x+iy, we get x= 0, y = 0... View Article

The Equation Z I Plus Z Plus I K Represents An Ellipse If K Equals

Solution: Let z = x+iy Given |z-i |+ |z+i| = k |x+iy-i |+ |x+iy+i| = k Taking modulus √(x2+(y-1)2)+ √(x2+(y+1)2)... View Article

If The Imaginary Part Of 2z Plus 1 By Iz Plus 1 Is 2 Then The Locus Of The Point Representing Z In The Complex Plane Is

Solution: (2z+1)/iz+1 Put z = x+iy (2(x+iy)+1)/(i(x+iy)+1) = (2x+2iy+2)/(ix-y+1) = (2x+1+2yi)/(1-y+ix) = (2x+1+2yi)(1-y-ix)/(1-y+ix)(1-y-ix) Given imaginary part is -2. Consider the... View Article

For Any Integer N Arg Root 3 Plus I 4n Plus 1 1 I Root 3 4n Equals

Solution: z = ((√3+i)4n+1/(1-i√3)4n) = (2(√3/2 +i/2))4n+1/(2(½ -i√3/2))4n = 24n+1 (cos π/6 + i sin π/6 )/ 24n(cos π/3 –... View Article

The Inequality Z 4 Less Than Z 2 Represents The Region Given By

Solution: Given |z-4 | < | z-2 | Put z = x+iy |(x+iy)-4 | < |(x+iy)-2 | |(x-4)-iy | <... View Article

If Z 1plus 7i By 2 I2 Then The Polar Form Of Z Is

Solution: z = (1+7i)/(2-i)2 = (1+7i)/(4-4i-1) = (1+7i)/(3-4i) = (1+7i)(3+4i)/(3-4i)(3+4i) = (-25+25i)/25 = -1+i a= -1, b = 1 r... View Article

If X Equal A Plus B Y Equal A Alpha B Beta And Z Equal A Beta Plus B Alpha

Solution: Given x = a+b, y = aα +bβ and z = aβ+bα α,β are cube roots of unity. So... View Article

If Fx Equal 4x 5 Plus 5x 4 8x 3 Plus 5x 2 4x 34i And F

Solution: Given f(x) = 4x5+5x4-8x3+5x2 +4x-34i f((-1+√3i)/2) = a+ib Let (-1+√3i)/2 = w ω3 = 1 ω+ω2 = -1 f((-1+√3i)/2)... View Article

If Cube Roots Of Unity Are 1 W W 2 Then Roots Of The Equation X 1 3 Plus 8 Equal 0 Are

Solution: Given (x-1)3+8 = 0 (x-1)3= -8 (x-1)= (-8)1/3 = 81/3 (-1)⅓ x-1 = 2(-1, -w, -w2) x = 1+2(-1,... View Article

If A Equal Cos Alpha Plus I Sin Alpha B Equal Cos Beta Plus I Sin Beta C Equal Cos Gamma Plus I Sin Gamma And A B Plus B By C C By A Equal 1 Then Cos

Solution: Given a = cos α + i sin α b = cos β+i sinβ c = cos γ+ i... View Article

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