Find the centre and radius of the circle formed by all the points represented by z = x+ iy satisfying the relation = k (k +1), where a andB are the constant z -B complex numbers given by a = C1 + ia2, B = B1 + iß2.

Q: 2. (a) Show that the points (-2x, 5x), (0, 4x), (6x, x) are collinear.

A: Given that: (-2x, 5x), (0, 4x) , (6x, x)

Q: Give the dual of the phrase "three collinear points and a fourth point not on the line of the other…

A: Dual of any phrase can be find by replacing the conjunction connective with disjunction connective…

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: Describe the set of points in the complex plane satisfies Z? + Z2

A: Introduction: The sum of a real and an imaginary number is a complex number. A complex number is…

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

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Q: Find a parametrization for the line segment beginning at P,(4, - 7,- 7) and ending at P2(0, - 7,2).

A: The line segment beginning at P1&lt;4, -7, -7&gt; and ending at P2&lt;0, -7, 2&gt;

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

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Q: Convert the point (r, 0, z) = 37 5, 3) to Cartesian coordinates. Give answers either as expressions,…

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Q: Find the equation of the plane that passes through (9, 13, 4) and is parallel to x + y + z = 3.…

A: Here we have to find equation of plane passing through a point (9,13,4) and is parallel to x+y+z=3…

Q: Verify the points (1,5) ,(2,3) and (-2,-1) are collinear or not

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

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Q: Find the distance from the point (3, -4, 2) to the yz-plane

A: We have to find the distance from the point 3,-4,2 to the yz-plane. We know that if any point px,y,z…

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: What is the image of the point (3,-6) after a rotation of 90° counterclockwise about the origin?

A: Consider the given point 3,-6

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: Show that the distance between the two points z1 and z2 in anArgand diagram is | z1 - z2 | .

A: Argand diagram:  1 It is a plot of complex numbers as point.  2In the complex plane using…

Q: find the distance in space between the points (5,3,-2) and (0,0,1)

A: Use distance formula between two points

Q: Prove that the point 2a +b-c, 5a -b+ 2c and 8a – 3b+5c are collinear.

A: Given, 3 vectors or points, A(2,1,-1) B(5,-1,2) C(8,-3,5)

Q: Find all planes in R3 whose intersection with the xz-plane is theline with equation 3x + 2z = 5.

A: Find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: 6. Center at (2,-3), one corner of auxiliary rectangle at (-1,-5), conjugate axis is horizontal

A: Given: Center: (2, -3) One corner of auxiliary rectangle at (-1, -5), conjugate axis is horizontal.…

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: What is the dual of the phrase “three collinear points and a fourth point not on the line of the…

A: Answer :  Dual of any phrase can be find by replacing the conjunction connective with disjunction…

Q: Compute the original coordinates with respect to x and y axes if the translated coordinates of this…

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Q: 2. Prove that (0, -2), (-4, 8), & (3, 1) lie on the circle with center (-2, 3).

A: We can use one of the given points to compute the radius and after that plugin each of the two other…

Q: z= 2e'+i

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Q: What is the image of the point (3, -4) after a rotation of 180 counterclockwise about the orgin

A: When rotated by 180 degree counterclockwise (x,y)-&gt;(-x,-y)

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

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Q: The distance from the point K(3, -2, 0) to the xy-plane is Select one: 3 -2

A: Find out the correct option.

Q: What is the image of the point (4, 0) after a rotation of 90 counterclockwise about the origin

A: Under rotation 90° counter clockwise about the origina point (x,y)→(-y,x)Hence (4,0)→(0,4)

Q: find the pole and resuidue of 3z + 1 (z + 1)(2z – 1)

A: Poles and residue of the given function are given below ;

Q: Make a general statement regarding invariant points after a reflection in the x-axis and then in the…

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Q: Which of the following is the equation with center (-9, 8) Major axis = 10? %3D 20 and minor axis…

A: To find the equation of the vertical ellipse with center (-9,8) . Major axis = 20 and minor axis =…

Q: Compute the intersections of the curve xy = 1 and the lines x +y = 5/2, x+y = 2, x+y = 0, x=0 , x=1…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: What is the image of the point (6,-3) after a rotation of 180° counterclockwise about the origin?

A: Our Aim is to tell the image of the point (-6,-3) after a rotation of 180°counterclockwise about the…

Q: Find an equation for the plane in R® spanned by the points (1,5, 1) and (1, 4, 2).

A: We have to find the plane equation for two given points

Q: Find all yy such that the distance between the points (3, -8) and (-10, yy) is 19

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Q: Find the distance from the point (5, 4, 3) to the plane −4x−1y−1z=4.

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Q: Determine the set of points satisfying the condition described by |z – 3| + |z + 3| = 10 Then…

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Q: Between each pair of points on the coordinate plane. Sin Ə 1. А(12, —2) and B(10, -2) 2. C(9,–3) and…

A: Note:- this is multiple sub parts question. According to our company norms i am solving here first 3…

Q: Find the distance from the point (-2, 1, 4) to the plane x = 3

A: Given: The point -2,1,4 and plane x=3 To find: Distance from the given point to the given plane.

Q: Find the distance between the point (1,3,-1) and the plane 3x - 4y + 5z = 6. (Enter an exact answer…

A: Given point 1,3,-1 and the plane 3x-4y+5z=6

Q: What is the image of the point (-7,9) after a rotation of 270 counterclockwise about the origin

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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: The plane containing the three points (2, –1, –1), (2, 1, 8) and (1, 0, 6). Please write th

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Q: Find the distance from the point (-1,4,5) to the plane 3x+2y-4z=5?

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