5) Let z, and z, be two non real complex cube roots of unity and |z – z| + |z – z3ľ = 1 be the equation of a circle with z,, z, as ends of a diameter, then the value of å is (A) 4 (В) 3 (C) 2 (D) 2

Q: Find and sketch the sets in the complex plane given by (1) z – 3|+|2+ 3=10 IZ (2) |Arg(z)|< t/ 2

A: here we can use directly definition or properties of curve to find that which curve is represented…

Q: The conditions to test the positivity of symetric quadratic form of four variables are f(1,0,0) 2 0,…

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Q: 8 If C is a circle of radius r with centre z,, in the complex z-plane and if n is a non-zero…

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Q: Sketch the in the Complex Plane curve given by /z-3) - 1z+3i/

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Q: 3. Plot the set of points in the complex plane which satisfy |2z + 3 – 4j| > 3.

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Q: 9. Give a geometrical interpretation of the intersection of the planes with equations x+y-3=0…

A: Give a geometrical interpretation of the intersection of the planes with equation. x+y-3=0 y+z+5=0…

Q: 4 Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0, z+x3=0,…

A: Find the four vertices of the tetrahedron.  Making four equation.  Then write it in matrix form.…

Q: 2. ( eMsa lan--a22 3. All 2-tuples representing points in the first quadrant of the plane including…

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Q: 2.2 Find upper bound of 2+4 (z - 3i)3 +1 where C is the circle |2 – 3i| = 4.

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Q: 6. Given a rule x2 + y2 = 9, its image rule x2 + y2 – 2x + 6y + 1 = 0 under a translation, state a…

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Q: 16- Find the equation of the plane that contains the line = 2+ = 5-z, and the point P(0,5,2).

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Q: Show that [o 2] A 3 0 has no A = L-U factorization where L is lower triangular and U is upper…

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Q: Describe the following points on the complex plane: (f) i3z = 2-',

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Q: 5. Consider two distinct points [b1 in the and plane. Explain why the solutions of the equation det…

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Q: 4) Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0,…

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Q: (b) Show that the equation e- - 2:2 = 1 has exactly two solutions in the disk |2| < 1, and that they…

A: Rouche's theorem: Let f and g be holomorphic function in the region D. Suppose gz&lt;fz on the…

Q: 7. Show that the equation of the plane that has x-intercept a, y-intercept b, and z-intercept c…

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Q: 7.46. Evaluate 2z² +5 (z+2)³(z²+4)2² C 2+2i, 1+2i. dz where C is (a) |z-2i = 6, (b) the square with…

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Q: Q, : Describe the set of points in the complex plane that satisfy z +1| (2) - = 2 z -1 11-1 =1리 (1)

A: Given that  1)z=z-i2)z+1z-1=2 Find out the set of points

Q: The distance from the point K(3, -2, 0) to the az- plane is Select one: O-2 O √13 O 0 02 O None of…

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Q: State where in the ty-plane the hypotheses of the Existence and Uniqueness Theorem are satisfied for…

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Q: Find the locus of the set of points z in the complex plane for which z - 4 4 Iz +6-+ t| %3D

A: Use the property z1z2=z1z2 and z=x2+y2. Take z=a+ib. So,  z-4z+6+i=4z-4z+6+i=4

Q: Q1: Formulate the equation of plane in space that contain two points (2,4,-1) and (1,3,-2) and…

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Q: 3. Find the constants bo, co, a1, b1, C₁ so that So(x)=1+ box + cox² + x³, S(x) = { S₁(x) = a₁ - 2x…

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Q: Prove that the circles x² + y2 + z2 - 2x + 3y + 4z - 5 = 0, 5y + 6z +1 = 0 x² + y2 + z2 - 3x - 4y +…

A: We will use equation of sphere passing through sphere S  and plane P  S+λP =0

Q: 2 b) Prove that Imz=0, larg z - 41= 4, 2-ž =0, 1Z-il=1Ztil are different equations all describing…

A: If we let z=x+iy then We will show that y=0 which is the equation of real axis.

Q: 2.2 Find upper bound of 2+4 (z – 3i)³ + 1 where C is the circle |z – 3i| = 4.

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Q: Let z2T3-L p=S+Si O fird all the complex mumbers %3D guien by hza

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Q: 2. Show that ( 1, 6), (0, 3), (1, 2), and (2, 3) lie on a common parabola.Hint: For scratch work,…

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Q: 13. Prove that the three points (-3, 2, 4), (6, 1, 2), and (-12, 3, 6) are collinear by using the…

A: To solve the following problem

Q: Suppose there are three planes in R^3. These three planes could intersect at a single point. What…

A: Any three planes considered at random in space R3 can either intersect or be parallel. There can be…

Q: Show that (−1, 6), (0, 3), (1, 2), and (2, 3) lie on a common parabola.Hint: For scratch work, plug…

A: Consider the three points (−1, 6), (0, 3) and (1, 2). Substitute the above three points in the…

Q: Describe the set of points in the complex plane that satisfy z + (2)- |1– |

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Q: 3 If C is a circle of radius r with centre z, in the complex z-plane and if n is a non-zero integer…

A: Consider the given integral as, ∮dzz-z0n+1

Q: 2. Use analytic geometry to verify that quadrilateral JKLM is a parallelogran 1C). YA K(-1,1) 2 -2 0…

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Q: 4. (5) Find the equation of the plane passing through the points. Simplify the equan (2,0,1),…

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Q: Give equations for two distinct planes whose trace in the xy-plane hasequation 4x + 3y = 8.

A: Given information: The xy-plane has equation 4x + 3y = 8. Calculation: The equation of the plane is…

Q: Reduce the equation    4x^2 + y^2 + 4z^2 - 4y − 24z + 36 = 0    to one of the canonical forms of…

A: Reduce the equation    4x^2 + y^2 + 4z^2 - 4y − 24z + 36 = 0    to one of the canonical forms of the…

Q: 1. Find the three cube roots of z =-j and sketch the result in a single Argand plane. (express…

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Q: What is the midpoint between z1 = 9i and z2 = 4? (2, 4.5) (-4,-9) (-2,-4.5) (4, 9)

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Q: The distance from the point K(3, -2, 0) to the xz- plane is Select one: O-2 O √13 O 0 02 None of…

A: We need to find out the distance between the given point and xz plane.

Q: 7. In quadrilateral FGHJ, FH and GJ bisect each other and FH = GJ. FG JH FJ GH What additional…

A: FH and GJ are bisector of each other.

Q: Let y = Vxy, y(xo) = yo- %3D %3D Find all points (x0, yo) in the xy-plane where an existence and…

A: Given that  Y'= √xy Y(Xo) =Yo

Q: 3 Find the e qu.of Plane that Contains elol; 3) and Parallel to the X-2 Plane and PerPendicular to…

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Q: A natural cubic spline is defined by [a, (x – 1)' + b, (x – 1)² +c, (x – 1) + d, f(x) = if 0<x<1 (x…

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Q: The distance between the centers of the following two spheres: x2+56x+y2−54y+z2=−1512,…

A: A detailed solution is given below

Q: 3. Find all the roots of z³ + 1 = 0 and sketch them on the Argand plane

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