Let z, and z2 be two complex roots of the equation z2 + az + b = 0. Assume that the Origin, z1, and Z2 are vertices of an equilateral triangle. Then, a2 = 4b a? = 3b a? = b a? = 2b

Q: Q2\ If z = 1 + i, what is z3 + z? + z + 1 as a single complex number?

A: Use the following formulae, to simplify the given expression.…

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

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Q: Find all the solutions to z6 = 1 − i√3, and plot them on the complex plane.

A: We will find out the required values.

Q: Consider the complex number z = (1 – i)(-1-iv3). Find |2| and arg(2).

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Q: Let a, b, and c be any three nonzero complex numbers. If |z| = 1 and 'z' satisfies the equation az +…

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Q: If a2 1,Find all complex numbers z which satisfy the equaution z +a| z +1+i=0.

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Q: 2. If a and b are complex numbers, and z is a complex number that obeys |z| = 1, show that az + b =…

A: Given that a,b and z all are complex numbers.   let, a=c+idb=r+is  and z=x+iy, where c,d,r,s,x,y all…

Q: Let a = v3 – i and b = -1+i be two complex numbers. (9a) | Compute the value of b18 z = aT (9b) |…

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Q: Find the product of the complex numbers: z, = -V3+3i and z2 =1+ 2i in polar form.

A: Given:          z1=-3+3i          z2=1+2i         product of complex number =z1×z2…

Q: Find all complex roots of the equation z6+z5+z4+z3+z2+z+1=0.

A: The given equation is z6+z5+z4+z3+z2+z+1=0    .....(1) We know that  z7-1=(z-1)(z6+z5+z4+z3+z2+z+1)…

Q: (a) The complex conjugate of 2 + 3i is 2 + 31 = (2 + 3:)(2 + 31) = [ (ь)

A: To find the complex conjugate.

Q: The complex number Z1and Z2 are given by, Z1 = 3 – 5i and Z2 = -1+ 4i Determine: 2Z1 +5Z2

A: We have to determine 2Z1+5Z2 for the given complex numbers: Z1=3-5i and Z2=-1+4i Finding 2Z1:…

Q: Find the roots of the given complex number 1. z^3 = -2

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Q: Let a = V3 - i and b= -1+i be two complex numbers. (9a) Compute the value of 618 = Z a7 (9b) Find…

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Q: Solve the equation z + z=0,where z is a complex number.

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Q: Find the complex number z that satisfies 3z + 5z = |2|2 + 8i.

A: The given problem is to find the complex number which satisfies the given complex function, We have…

Q: Find all solutions w to the equation w = 4b2.

A: As per bartleby guidelines we are supposed to answer only one question per post. This post contains…

Q: Q2- The complex number z satisfies the equation 4Z- 32 %3D 2-1 1-181 Then Z = ......... ..*......

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Q: z1 = 2 + 4i Z2 = 5e2i %3D Z3 = 4 cis 40° %3D

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Q: Find the complex conjugate z, of z1 = -4i + 4. ž =

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Q: If z and z are conjugate complex numbers, find two complex numbers, z = : = z; and z = z,, that…

A: Note some result about complex number : Suppose z is a complex number then there exist a,b∈ℝ such…

Q: If 'a'is a complex number such that z = 1. Find the value of a, so that the equation az? +z+1=0 has…

A: Explanation of the answer is as follows

Q: Find the value of z and w in the following simultaneous equations 3z + 6 = -iw 2z – 4 = w + 2i Also…

A: 3z + 6 = -iw 2z - 4 = w + 2i

Q: The complex number Z1 and Z2 are given by, Z1 = 3 - 5i and Z2 = -1+4i %3D Determine: 2Z1 +5Z2

A: topic - complex numbers

Q: 3.) 71 + z2 – Z3 + Zz

A: Given problem is solved below in detail

Q: Let x₁, x₂ are the roots of the quadratic equation x² + a where a, b are complex numbers and y₁, y2…

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Q: Find all the roots of the given complex numbers a) z5 = -32 b) z² + (i – 2)z + (3 – i) = 0

A: To find - Find all the roots of the given complex numbers z5 = -32 z2 + i - 2z + 3 - i = 0

Q: (a) Find all roots of the quintic equation, in the complex plane and plot them. 25 -1 = 0,

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Q: and of b is Writing the complex number z=2 e6 in the form a+ ib, the value of a is

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Q: Find the product of the complex number z = 3 + 4i and its conjugate z*.

A: The complex number is given as z=3+4i

Q: Draw all eight solutions of z8 = 1 in the complex plane. What is the rectangular form a+ ib of the…

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Q: Show that root of following quadratic equation are complex numbers a. 2x2 + x + 3 = 0 b. 7x2 + 5x +…

A: Compare the equation 2x2+x+3=0 with the general form of the quadratic equation ax2+bx+c=0, to find…

Q: :If z is a complex number satisfying the equation (-1)" = =", where n e N. Show that the locus of z…

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Q: Solve the equation: z* = 8 V3 + 8i and draw the solutions in the complex plane by using Mathematica.

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Q: it is given that z+2i=iz+A, w/z=2+2i, Imw=8, where z and w are complex numbers and A is a re…

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Q: 2) Find the sojution in the field of the complex numbers to the linear equation 2x- (1+ 2i) =-ix +…

A: Step:-1 Given that  2x - 1+2i = -ix + 2+2i right all terms of x in left side and constant terms in…

Q: The reciprocal of a complex number x+jy is

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Q: Solve the following equation in the complex number system. Express solutions in both polar and…

A: Given  Z1=2+4i Z2=5e^2i Z3=4 cis 40°

Q: Given the complex numbers z1 = -3+i and z2 = 1+ 4i. Show that |z1 z2 = |z1||22| and org (z1 2) = arg…

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Q: Find all complex solutions of x-5x+7=D0. (If there is more than one solution, separate them with…

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Q: Let a = v3 – i and b = -1+i be two complex numbers. (9a) Compute the value of b18 2 = a7 (9b) Find…

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Q: Find the cube root of -8i lying in the fourth quadrant of complex plan. إختر أحد الخيارات: 1- V3i 1+…

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Q: Q4\ If z and z are conjugate complex numbers, find two complex numbers, z = z, and z = z,, that…

A: The given equation is: 3zz¯+2z-z¯=39+i12 Let z=a+ib be a complex number satisfying the equation,…

Q: : If z is a complex number satisfying the equation (=-1) = =", where ne N. Show that the locus of z…

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Q: How many complex numbers satisfies both equations, z – i| = 2 and |z – 4i| = 1?

A: We know that z=x+iy, then…

Q: What are all the cube roots of -1 in the complex plane? Mutiple choice options: 1 -1 e(5π / 3 i)…

A: Given problem:- What are all the cube roots of -1 in the complex plane?   Mutiple choice options:…

Q: If the complex number z = x + iy is a solution of the equation z2 + z + 1 = 0 then show that z = x…

A: z2 + z + 1 = 0 Solve the given equation using quadratic formula…

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