Find the locus of the points z that satisfies 3(22 + z?) + (8 – 16i)z + (8+ 16i)z – 10|z|? = 16.

Q: Prove that the three points (;q, yx), (x2, y2), and (x3, y3) are collinear (lie on the same line) if…

A: Given : The three points are : x1, y1, x2, y2 and x3, y3 Now we have to prove that  x1, y1, x2, y2…

Q: Write y as an affine combination of the other points listed. 1 1 5 1 4 - 5 y = -29 %3D V2 V3 2 - 2 1…

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Q: Express K#S^2#T#2P as a connected sum of projective planes or as a connected sum of tori.

A: To express the given connected sum (of surfaces) in the required form

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

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Q: Find a plane containing the point (7,-8,8) and the line F(t) = +t

A: Given that, the point is 7,-8,8 and the line is r→t=-6,-8,-7+t6,8,4. From the given line, the point…

Q: ?, R(A)IN(A*)

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Q: Find the Cartesian equation of the locus of z where |z – 1- i| = |z – 1+ 2i|

A: Cartesian equation

Q: Find all numbers z such that Az3 + Bz² + Cz = D %3D B = [2 4 21 1 1 1. A = 1 3 1. 1 -2 2 4 21 C li 3…

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Q: Draw a picture on the z-plane

A: In this question, we draw a picture of the given curve in C(t). here, first, we write the real and…

Q: 5. The ends of the transverse axis are at (+8,0) and the ends of the conjugate axis are at (0. 16).

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Q: 3. If a plane contains two distinct points Pi and P2 then show that it contains every point on the…

A: Solve the given

Q: (c) Compute the distance in AU between the points (x,0) = (1.24,0) and (1.24, 7)

A: Given: The coordinate transformation, x=Rsinhχsinθcosϕ y=Rsinhχsinθsinϕ z=Rcoshχcosθ The plane…

Q: 6. Prove that (i) the three points A(1,4,2), B(3, 2, 4) and C(5,0,6) are collinear, (ii) the four…

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Q: Find midpoint M of P,P2, which joins P1(5, -7, 2) and P2(2, 5, 6), as shown in Figure 10.46 of…

A: Formula used : Mid-point formula Mx1+x22,y1+y22,z1+z22 Here (x1,y1,z1) and (x2,y2,z2) are the end…

Q: (a) y= -2 (d) xy = 0

A: Consider the given information.(a)The given condition is y=-2.The line y=-2  is a vertical line,…

Q: Prove that (X + Y) (X+Y) = X

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Q: EX Find the reglon in the z-plane represented bye

A: Given

Q: Give a geometric description of the set of points (x, y, z) satisfying the pair of equations z = 0…

A: given: the set of points (x,y,z) satisfying the pair of equations z=0 and x2+y2=1. as we know that…

Q: 28. The locus of the points z such that /z 3/ = 2 is A. x² + y = 4 C. x* + y - 6y + 5 = 0 D. x+ y-…

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

Q: Cemplex Fur O Express the following functrous in the form u+iv fCz)= 2iz +6 Z* of(2)= é • f(2) = In…

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Q: A(n)________ is the collection of points in the plane the difference of whose distances from two…

A: The given statement is "A(n)________ is the collection of points in the plane the difference of…

Q: Find the locus of the points P(x, y) such that PA = 2PB where A is the point with coordinates (0, 3)…

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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 fxTy and f,, and evaluate each at the given point. (x, y, z) = x2y3 + 2xyz- 4yz, (-2, 1, 2) %3D…

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Q: Prove that H(x, y) = (x, –y) provides a conjugacy between x' = (4 })x and Y'= (; 7). X and Y' = 1 -1…

A: Given: X' =11-11XY' =1-111Y To prove: H(x,y) = (x , -y) provides conjugacy between both of the above…

Q: graph the points z = x + iy that satisfy the given conditions. 5. |z + 1| = 1 6. |z + i |= |z - 1|

A: Hi there, at a time we can answer only one question at a time and the exact one was not specified.…

Q: In the Argand's plane what is the locus of [3(22²-5z + 3) 11_2π ong

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Q: prove Theorem 4P.1 Theorem 4P.1 There are exactly six lines in the four-point geometry.

A: The known fact is that in four point geometry, any two distinct points have exactly one line on both…

Q: (2) Let P = (1, 1), Q = (4, –2) and R = (2,3). Find the point S such that R$ is equivalent to PQ.

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Q: 1. Determine the equation of the locus of the point which moves so that the sum of its distances…

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Q: Graph the points z=x+iy in |z|

A: Given z=x+iy The graph of z=x+iy  and |Z| is

Q: Find t for the following terminal points: (a) P(0, 1), t = (0) P(-, ), t =| (c) P(-1,0), t = (d)…

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Q: 3. If a plane contains two distinct points P1 and P2 then show that it contains every point on the…

A: The given problem can be proved both by mathematically and by the definition. For your convenience I…

Q: 3. The vertices of AFGH are F(-1, 1), G(-5, 4), and H(-5,-2). X is the midpoint of FG, and Y is the…

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Q: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…

A: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…

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: Prove that if P(I, y) be any point on the line segment joining R(11, Y1) and P2(12, Y2) then I= I1+…

A: Let P divides P1 and P2 in the ratio k : (1-k) x=kx2+1-kx1k+1-kx=kx2+x1-kx1x=x1+kx2-x1 Similarly…

Q: Determine the quadature rule of the form | f(r) dr = Aof(ro) + A1f(£1) + - *·+ Anf(Tn) a. when the…

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Q: 12. Let v =|0 and y For what value(s) of h is y in the plane -3 -2 generated by v and v2?

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

Q: 3 Show that the planes, x-2y+4z-13D0 and 3x-6y+8z=5, if so, find the distance * .between them…

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Q: Theorem 4P.1 There are exactly six lines in the four-point geometry.   proof the Theorem 4P.1 by…

A: To prove that in the Four point geometry , there are exactly six lines: the proof should be based on…

Q: 6. Prove that (i) the three points A(1, 4, 2), B(3,2,4) and C(5, 0,6) are collinear, (ii) the four…

A: Given: i) A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6) ii) P(2, -1, 1), Q(1, 3, -2), R(-2, 1, -3), and S(3,…

Q: Describe geometrically the set of points z satisfying the following condition:|z−2i|=3 .

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: Describe geometrically all points P(x, y, z) that satisfy the given condition. X = 1

A: Given the points P(x,y,z) that satisfy the condition x=1.