In the Argand diagram points A, B, C, D represent the complex numbers a, B, Y, 8 respectively. (a) If a+y= B+8 show that ABCD is a parallelogram. (b) If ABCD is a square with vertices in anticlockwise order, show that y+ia=B+iß

Q: Write the coordinates of the vertices after a rotation 90° counterclockwise around the oric 10 V. 4…

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Q: How many complex numbers satisfies both equations, Iz- il = 2 and |z- 4i|l = 1?

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Q: 0, : Describe the set of points in the complex plane that satisfy |!- |=|| (1) (2) Q. : Write the…

A: As per our guideline we are supposed to answer only first question of a multiple type questions.…

Q: In an Argand diagram a set of points representing complex numbers z is defined by the equation |z-…

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Q: Describe geometrically (or make a sketch of) the set of points z in the complex plane. |z-2i| ≤ 3

A: Let z=z+iy∴z-2i=x+iy-2i   z-2i=x+iy-2∴z-2i=x2+y-22

Q: If z,,z, are two complex numbers then: ||z.|-|z2||>|z,-z z. +z_ s z +z]. z +z_ = z +/z

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Q: Find all the roots in the complex plane using De Moivre's Formula in polar form and rectangular…

A: To find the fourth roots of -1 the De Moivre's formula convert the rectangular co-ordinate to polar…

Q: Given two complex number (2 + i) and (-3 + i), find the distance between the two numbers on the…

A: NOTE: Refresh your page if you can't see any equations. . two complex numbers are

Q: A vertex of hexagon is given by 0+i and the center is given at origin in the complex plane, find the…

A: To find coordinates of vertex of hexagon, given

Q: The distance between two points in the complex plane is the ________ of the difference of the…

A: Let (a,b) and (m,n) are two points in the complex plane. Then the difference of the complex numbers…

Q: | Re(z) |> 1 | 2 – i< 3 1</ z + i+1|< 2

A: As per our guideline we are allowed to do 1 question or maximum 3 subparts at a time. Please post…

Q: Find the distance between the complex numbers in the complex plane. 1 + 4i, -1 + 7i

A: The distance between the two complex numbers, z1=a+bi and z2=c+di in the complex plane is  In the…

Q: If the complex number z = x + iy satisfies the condition |3z – 6i| = 3 , then z lies on Oa. a.…

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Q: Sketch the in the complex curve plane given by.- i) |2 -31 12+3i/ %3D

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Q: Give all the elements of Ug and write them in rectangular form. Draw the regular octagon in the…

A: Note: Usually U8denotes {1,3,5,7} with multiplication operation but as per your notations it seems…

Q: Graph the complex number, find its modulus and put the complex number in polar form with arguement Θ…

A: -1 - sqrt(3)/3 i = -1 - 0.577i (approx) This is similar as (-1,-0.577). Plotted it on graph.

Q: Show that if z1 and z2 are complex numbers, then zi + z2 = Zī + Z2.

A: Suppose the two complex numbers are z1 and z2 such that where a,c are real parts and b,d are…

Q: Pick two complex numbers (like a + bi and c + di) and consider if the following statement is True or…

A: Set of pure imaginary numbers

Q: V-1, is If x1 = represented by the point A (4, -3) in the x-y plane shown below. If point B, not…

A: The correct answer is 26.2 (approx.)...see the attachment below for the detailed explanation

Q: P,Q,R,S are four non-collinear points in the Argand diagram, representing the complex numbers…

A: Given that z1, z2, z3, z4 are four non-collinear points in Argand plane. Consider a quadrilateral…

Q: Two points (4 + 7i)and (-3 – 7i) are in a complex plane. Find the magnitude of their difference.

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Q: then find (An B C). Z, +Z3 1-i3 Z2 - Z3 (B) right angled isosceles (D) obtuse angled 7. The complex…

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Q: If z is a complex number, show that the sum of z and its conjugate is a real number.

A: Given z is a complex number. Let z=x+iy We know that conjugate of a complex number is given by…

Q: If z is a complex number, show that the product of z and its conjugate is a realnumber.

A: Let z=a+ib be any complex number where a and b are real number. Then conjugate of z is z¯=a-ib

Q: If 21 and z2 complex numbers such that z1 = 1+ V3i and 22 = V3+ i determine in polar form, (i) ž122…

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Q: Argand plane. Label properly. 2. Represent the following complex numbers on one A = 1+1 B = 1- C =…

A: Given that: A=1+iB=1-iC=-3+4iD=-3-4i

Q: If a, B, Y, 8 are four complex numbers such that a+ Bt is real and od - By# 0, then z = Y+8t te…

A: We have given α, β, γ, δ are real numbers such that γδ is real number and αδ - βγ ≠0.

Q: 7. 1 + 을mi

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Given two complex numbers z and w such that z = (1+ i)w + (3 –- i)w, where w is the conjugate of w.…

A: z and w are two complex numbers. Such that

Q: Find the sum and the product of the given complex numbers. Plot a quadrilateral with the origin, the…

A: Given two complex numbers, z1=-3-i, z2=4+5i. We have to sum and product and plot them.

Q: Solve for the six sixth roots of z-1 and show their geometric representation on a single complex…

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Q: 11. The vertices of an equilateral triangle are equidistant from the origin. One of its vertices is…

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Q: Plot the points z = 3+9i and w = 7+5i on a complex plane ană find distance between

A: Plot the points z = 3+9i and w = 7+5i

Q: Find and graph all the roots in the complex plane. 3. (3+ (4)

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Q: Find the midpoint of the line segment joining the points corresponding to the complex numbers in the…

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Q: Draw the triangle with vertices 21 = 2 – 4i, z2 = -5 – 4i and z2 = plane and also find the area of…

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Q: Find the distance between the complex numbers in the complex plane. 71, 4 - 3i

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Q: Ecample 12: Show that the equation of a straight line in the Argand plane can be put in e form zb +…

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Q: On an Argand diagram the points A, B and C represent the complex numbers a, ß and y respectively.…

A: ARGAND DIAGRAM The point represented by a+z-aeiθ is a rotation by θ anticlockwise about the point…

Q: Suppose Z, and Z, are two given complex numbers. Construct graphically a. 3Z1- 2Z2 b. (1/2)Z,…

A: Suppose complex number Z1=a1+ib1=2+3i and Z2=a2+ib2=-1-2i (a) given complex number 3Z1-2Z2…

Q: Find the distance between the complex numbers in the complex plane. -2 6i, 6 + 5i

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Q: Two points 4+ 7i and -3 – 7i are in a complex plane. Find the magnitude of their difference.

A: Explained below...

Q: Find all points on the complex plane which represent the complex numbers w = (V3- 1)z+1-2i, given by…

A: We know that, z=2eiϕ, ∀ϕ∈ℝ implies the circle of radius 2 with center at origin. Graphically: Now,…

Q: Show that if z1 and z2 are complex numbers then (z1/22) = Zī/22.

A: Given, z1 and z2 are two complex numbers and we have to show,

Q: Find the distance between the complex numbers in the complex plane. -2 - 4i, 4 + 7i

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Q: Two points 4 + 7i and -3 – 7i are in a complex plane. Find the magnitude of their difference.

A: To find: The magnitude of the difference of two complex point. Given information: The two points in…

Q: If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on Select one: х…

A: Given that: z=x+iyCurve: |z+1|=1

Q: 1. If Iz| = 2, then find the locus of complex number (a + bz), where a, be R.

A: If |z|=2, then find locus of a complex number a+bz

Q: If the complex number z and its conjugate z' satisfy zz' + 2(z - z') = 12 + 8i, then the values of z…

A: Explanation of the answer is as follows