A(n). number is a number of the form a + bi where a and b are real numbers and = -1. O substitute O imaginary concept complex

Q: .1 Determine the possible values of xif 2x|2|x-3|. Hence, give your answer in interval notation. 2…

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Q: Let z be the solution to z2 16 with - Im(z) > 0, and let w be the solution to w? 64 with Im(w) > 0.…

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Q: Find w a + bi = where a and b are real number N -48+14i W3= w3=

A: Let us consider, z=-48+14i We have to find z. Let w=a+bi=z; where a and b are real numbers Then we…

Q: Let a, b, c be real numbers. If ax' + bx +c = 0 has two real roots a, B where a 1, then show that…

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Q: Find the k=8 root of the 10th root of 1+i. Express the answer in rectangular form in 4 decimal…

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Q: a. Show that If 1 iv3 z = 2 2 Then z7 = z. b. Evaluate all the roots of the Equation: z* + 16 = 0

A: We will solve both the parts only using some basic knowledge of complex numbers and their…

Q: 3. In the equation given below: 1- 5i y %3D 3— 21 2 -і Given further that x and y are an element of…

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Q: 1 was placed in the form ax where a and b are real numbers, then which of the 2x 3. If the…

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Q: 0. If x, y and z are real numbers and x y°z10 > 0, which of the following must be positive?

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Q: (e) Determine exact expressions for the real and imaginary parts of z.

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Q: Find x so that the distance between (−2, 6) and (x, 4) is square root of 29. .  (Enter your answers…

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Q: 5. Simplify to a C. Write answers in the form a + bi a, beR (g) (1+3i)(1 – 4i) (h) (5 – 2i)(-1+ i)…

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Q: prove it :     ( 1/2 + 1/2i )10 = 1/32i

A: Use the properties of complex number to solve this problem.

Q: Find two positive real numbers x and y such that their product is 2450 and x + 2y is as small as p…

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Q: D Express the following 3 complex form; e u! wof Jejod u! !h + e b.) -3+4:

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Q: Which of these equations has two real roots: Select one: O a x2 - 4x + 4 =0 O b. x2 - 10x + 100 = 0…

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Q: Which statement best describes the roots of f (x) = x* O 1 real, multiplicity of 3 O 2 real, 1…

A: Solve the following

Q: Evaluate x - 2x +2 for x = 1 + i. x - 2x +2 evaluated for x =1+ i equals (Type your answer in the…

A: To evaluate x2-2x+2 for x=1+i

Q: 5. Find real numbers a and b such that (1 + 5i) · (a + bi) = 1.

A: A complex number is a number of the form a+bi where both a,b are real numbers. The number i is the…

Q: x +x +9x+9 = (x+a)(x+ bi)(x-bi), where a and b are real number constants and b> 0. %3D If the…

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Q: How many positive real roots are there in the equation 7x²+5x+3x²+x=0? a. 2 b. 0 C 3 a. 144 b.…

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

Q: EXAMPLE 5 Using Square Roots of Negative Numbers Evaluate (V12 – V-3)(3 + V-4), and express the…

A: The given expression is, 12--33+-4 On simplifying the terms, we get…

Q: Find real numbers a and b such that the equation is true. a + bi = 2+6i a = 3,6 = 2 a = 5,6 = 9 a =…

A: To find the values of a and b.

Q: Suppose a quadratic equation is given as follows: k – 1)x² + x +1 = 0 Select all values of k for…

A: To get Complex conjugate root it's discriminant must be negative

Q: Do not use a calculator in this question. Find the positive value of x for which (4 + V5)x² + (2 –…

A: 3 Given equation is 4+5x2+2−5x−1=0. We have to find the positive value of x. The solution of the…

Q: Define a homegrnous ystem of lincar equations with's equations Snd t moke enmouns, (This is meant to…

A: We will first define what is a linear homogenous equation then we will given the definition  of…

Q: v) Fimd Find y as a function of t if 4y" + 36y' + 83y = 0, y(0) = 4, y' (0) = 8. y = Note: This…

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Q: The roots of 6x2 +7x + 34 = 0 are: O Real and Equal O Real and Distinct O Complex and Unequal O…

A: To find the behaviour of the roots of the given equation.

Q: I. Solve using De Moivre's Theorem. 1. Find the real values of x and y such that (x + y)³ is greater…

A: We need to find the values of x and y, such that (x + y)3 is greater than 8.  Let us take x =…

Q: 15. Find the two square roots of the following and write your answer in standard form. 2+ 2iv3

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Q: Find non-zero real number values of a, b, c, and d such that the sum (a + bi) + (c + di) is... -a…

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Q: 25. Use the value of the discriminant to determine the number roots of 2 + 20 = 12x - 16. complex:…

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Q: Let x be any real number. Also consider the numbers z = -2i(5 – xi)² y w=1+i, , then the value Im of…

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Q: A number of the form iy is called pure imaginary ylgn O İhi

A: A number of the form iy is called pure imaginary

Q: 16. Discriminant D = b´ – 4ac For y = ax“ + bx + c If D>0, there are two real roots If D=0, one real…

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Q: 10. Use i = (0, 1) and y = (y, 0) to verify that -(iy) = (-i)y. Thus show that the addi- tive…

A: i=0 ,1y=y ,0 verify :   -iy = -iy  To find additive inverse of z=x+iy

Q: What are the imaginary roots of the function in #20? f (r) = x³ + 2x2 + + 3x + 6

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Q: 5. Simplify to a C. Write answers in the form a + bi a, be R -8+ 3i (p) -9 – 5i V5 + 2i (q) 1- 2i 17…

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Q: Let A and B be real numbers such that a root of the equation z ^ 3 + Az ^ 2 + Bz + 26 = 0 is 1 + i.…

A: First of all, as coefficients A and B are real, we know that, if z ∈ C is a root of an equation,…

Q: 8. The number of roots of a complex is equal to the index of the radical sign True O False

A: The radical operation can also be performed for a given complex number. The nth radical of a complex…

Q: 6. Choose the correct answer. Which of the following equations has no real roots? O x² + 4x x² + 4x…

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Q: 7.For which value of k will the roots of 2x + kox+1 = 0 be real? .2 1) 1 2) 2 3) 3

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Q: Solve for x given that   x = a/b = b / a/4   where a and b are some given positive real numbers.

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Q: Solve the following equation for x. Let X= 2*. 2* - 40• 2 +256 = 0 X3= (Use a comma to separate…

A: Properties of exponent: 1) if am = an then m=n.

Q: Suppose z=2- 3i, What is a complex function f (z) =-3z - 2i Re (z) ? | | o 6-13i o-6-13i o 6+13i…

A: Anu complex number z is of the form z = x+iy, where x and y both are real number and i is square…

Q: A number of the form iy is called pure imaginary ylgn O İhi O

A: given a complex number

Q: 7. Which of the following most precisely describes the roots of the equation 3x2 + 4x -1 = 0? A 1…

A: Using quadratic formula

Q: + 9x +9 = (x +a)(x+ bi)(x- bi), where a and b are real number constants and b > 0. If the equation…

A: In the given question we have to find the values of a and b which satisfies the given equation for…

Q: Find real numbers a and b such that the equation is true. a + bi 3D 19 — 6і a = %3D

A: We can find the value of 'a' and 'b' as below