Solve the following equation by completing the square: x^2 + 6x +1=0. Write complex numbers in the form a+ bi form.

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

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Q: GIVEN COMPLEX NUMBER 1. - 5i?-3i =

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Q: What is the complex conjugate of 2 + 3i? What happens when you multiply this complex number by its…

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Q: Find the root's 51 of Complex equation:

A: Given:      5√(-1)

Q: Solve the equation x6 +1 = 0 in the complex number system. Express solution in polar and rectangular…

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Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-4 + 2i

A: z=-4+2i Now, r=-42+22=20=25 & θ=tan-1yx=tan-12-4=π-tan-112     ∵Given complex number lies in…

Q: Divide complex numbers: 3- 2i 2-

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Q: Simplify the complex number i ,65 as much as possible.

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Q: Solve x2 + 2x + 2 = 0 in the complex number system.

A: Explanation: Given that,  x2+2x+2=0   Concept Used: Quadratic formula- x=-b±b2-4ac2a

Q: Cannot solve

A: First we solve the equation for x

Q: How would I find the magnitude of the complex number based on the given values for z?

A: To find the magnitude of the complex number

Q: Extract the square root of the complex number 8-6i.

A: We have to find the square root of the complex number 8-6i.

Q: This complex number is pure real? 1-2i/i and why?

A: For a complex number, z=x+iy, where x is the real part, y is the imaginary part. The complex number:…

Q: sin(0.346 – 0.548i), |

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Q: Solve the equation x2 - 4x + 8 = 0 in the complex number system.

A: Given: x2-4x+8=0

Q: Solve the equation 2x^4-15x^3+24x^2+81x-260=0 giving all solutions in the complex number system

A: The given equation is,

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

A: Given  X6+64 = 0

Q: Solve for the value of each of the complex variable in the following equation. press your answers in…

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Q: Solve for variable in x^3 - i = 0 over complex number system

A: Let's solve given complex number equation.

Q: What is the complex conjugate of 2 – 3i ?

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Q: Without solving, determine the character of the solutions of the equation in the complex number…

A: Given the quadratic equation  x2 + 6 = 2x x2  - 2x + 6 = 0 By using discriminant, b2 - 4ac = (-2)2 -…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-5

A: Let  z = x + iy  then  z can br written as reiθ where r = x2+y2           θ = tan-1yx

Q: find all complex Solutions for.each equation by handa X+3 18

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Q: Solve the equation x6 - 1 = 0 in the complex number system. Express solutions in polar and…

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Q: Solve the equation x6 - 1 = 0 in the complex number system. Express solution in polar and…

A: Since the given equation has degree 6, it can be concluded that there are exactly six solutions.

Q: Is the sum of a complex number and its complex conjugate a real number?

A: Consider the given statement as "Is the sum of a complex number and its complex conjugate a real…

Q: Convert the complex number z = -√2 (lis (317) in its rectangular shape

A: Given: z=2cis3π4 To find: Rectangular form of given complex number.

Q: Without solving, determine the character of the solutions of the equation in the complex number…

A: Consider the provided equation, 2x2+3x=4 Without solving, determine the character of the solutions…

Q: R5 cis 1

A: Solved below

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-20i

A: -20i

Q: Solve the equation z – 8 = 0, giving the results as complex numbers.

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Q: Without solving, determine the character of the solutions of the equation in the complex number…

A: 3x2-3x+4=0 Comparing with ax2+bx+c=0, we get a=3,  b=-3  &  c=4

Q: Solve the equation in the complex number system. x + 3x +4 = 0

A: The given equation is x2+3x+4=0. Compare the given equation with ax2+bx+c=0. Here, a=1, b=3 and c=4

Q: Write the complex numberz=-4+4i in trigonometric form

A: polar form any complex no is given by as: z =r(cosx+i sinx)

Q: how do i solve this operation and express the answer as a simplified complex number ? step by step…

A: We need to simplify the given expression

Q: What is the cartesian form of the complex number: (-1-i√3)4

A: The given complex number: -1-i34.

Q: In the complex number system, x2 + y2 (the sum of two squares) can be factored as (x + yi)(x -…

A: To prove: x2+y2=x+yix-yi We know that a+ba-b=a2-b2 And we know that i2=-1 Solving the right hand…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.4 - 3i

A: Given: z=4-3i We know that any given complex numberz=a+ib can be written in polar form as below…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-6i

A: Express the complex number in trigonometric form with 0 ≤ θ < 2π.z=-6i=0-6i

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: Solve each equation in the complex number system. x2 + 3 = x

A: Complex numbers are those numbers which is represented in the form of a + ib where is a real part…

Q: How do I write this complex number in standard form?

A: Given that: -7.-14

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

A: We know that z=x+iy, then…

Q: Solve the equation x3 - (1 - i√3) = 0 in the complex number system. Express solution in polar and…

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Q: Find complex root of the equation =²+1=0

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