In the complex number system, x2 + y2 (the sum of two squares) can be factored as (x + yi)(x - yi).Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

Q: in the complex numbe 3 + 4i, the absolute value is:

A: Given that complex numbe 3 to find the absolute value

Q: Find all complex-number solutions by completing the square 2r2-3r=-7

A:

Q: Rewrite the quadric equation in standard form. 4x2 +9z2- 8x 36y-36z + 32 0

A: Given,          -4x2+9z2-8x-36y-36z+32=0

Q: Does the equation 4x2 + 20x + 25 = 0 have (a) two nonreal complex solutions, (b) two equal real…

A: 4x2+20x+25=0Formula: Discriminant, D=b2-4ac

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: What are the complex solutions for z2- 2 +5 = 0? 士

A:

Q: Find all real solutions of the equation.

A: 13x-12=2

Q: Solve the equation 4x2 - 4x + 5 = 0 in the complex number system.

A: The given equation is 4x2-4x+5=0. On comparing the given equation with the standard equation…

Q: What are the roots of the equation x2 - 16x + 65 = 0 in simplest a + bi form?

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Q: Select all the complex solutions for 2x² + 3x+ 9 = 0.

A: The equation is 2x2+3x+9=0. The quadratic formula for ax2+bx+c=0 is x=-b±b2-4ac2a. Here, a=2, b=3,…

Q: 4. Form the equation whose roots are the multiplicative inverses of the roots of 3x2 + 10x – 8 = 0.

A:

Q: Find all the complex solutions of the equation. x^6+64=0

A: Given equation is

Q: Solve for A. 2 -1 A = 1 0 -1 A = %3D

A: To find A

Q: Find all real and complex solutions of the equation 2x^2 +4x + 3 = 0.

A: Given: The equation, 2x2+4x+3=0.

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

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

Q: first use the discriminant to determine whether the equation has two nonreal complex solutions, one…

A: We have  2x2-6x+1=0   Compare with standard equation ax2+bx+c=0. Here, a=2, b=-6 and c=1…

Q: Solve for the roots  3x3-11x2+5x+3

A: We have to find the roots of the polynomial 3x3−11x2+5x+3. For the roots of the polynomial, solve…

Q: Does the equation 4x2 - 3x = -5 have (a) two nonreal complex solutions, (b) two equal real…

A: 4x2-3x=-5

Q: In the complex number system, find the complex solutions of theequation x2 + 2x + 2 = 0.

A:

Q: Consider the equation√2x + √1 = x - 7.Squaring the left side and simplifying results in________…

A: Given equation is 2x+1=x-7 Given equation can be written as 2x+1=x-7 Squaring the left side, we get…

Q: Solve for the roots   4x2-5x-2

A:

Q: first use the discriminant to determine whether the equation has two nonreal complex solutions, one…

A: The given equation is 8x2+18x-5=0

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

A:

Q: first use the discriminant to determine whether the equation has two nonreal complex solutions, one…

A: Given equation is: 4x2+20x+25=0We know determinant D of a quadratic equation of the form ax2+bx+c=0…

Q: first use the discriminant to determine whether the equation has two nonreal complex solutions, one…

A: Given: 3x2 +4x = 2 To solve: The given quadratic equation.

Q: What are the roots of the equation 16x - 64x + 65 = 0 in simplest a + bi form? %3D

A:

Q: first use the discriminant to determine whether the equation has two nonreal complex solutions, one…

A: 9x2-6x+1=0

Q: 3x2+8 ン

A:

Q: Use Descartes’ rule of signs to determine the number of possible positive, negative, and nonreal…

A: Descartes' rule of signs states that the number of possible positive real zeroes is equal to the…

Q: Find all real and complex solutions of the equation. x4 - 256 = 0

A: x4 - 256 = 0

Q: using the method of completing the square , show that the equation 4x2+3x+5=0 has no real roots

A:

Q: first use the discriminant to determine whether the equation has two nonreal complex solutions, one…

A: To solve the equation: x2+4x-21=0 Solution: We know, discriminant 'D' of a quadratic equation of the…

Q: Use the discriminant to determine whether the quadratic equation has two equal real number…

A: Use the discriminant to determine whether the quadratic equation has two equal real number…

Q: Express x2 + 6x + 16 in terms of a perfect square.

A: Given expression is x2+6x+16. Making the given expression as perfect square.…

Q: Use the discriminant to determine whether the quadratic equation has two equal real number…

A:

Q: first use the discriminant to determine whether the equation has two nonreal complex solutions, one…

A: Known fact: The quadratic equation ax2+bx+c=0 has two real different solutions if b2-4ac>0 . It…

Q: use the discriminant to help solve each problem. Determine k so that the solutions of x2 - 2x + k =…

A: Given equation: x2-2x+k=0 If descriminat D=b2-4ac<0 is negative, the equation has no real root…

Q: first use the discriminant to determine whether the equation has two nonreal complex solutions, one…

A: Given : The quadratic equation  x2 - 3x - 54 = 0 we have to tell using the discriminant to determine…

Q: What are the complex solutions to the following equation? 3x2 – 2x + 3 = 0 -

A:

Q: Find all complex solutions using an appropriate method. 6. x* – 7x² = 44

A:

Q: find the discriminant of each equation and determine whether the equation has (1) two nonreal…

A: Conversion of the given equation into the standard equation and formula of discriminant helps to…

Q: first use the discriminant to determine whether the equation has two nonreal complex solutions, one…

A: First checking discriminant of the equation x2-7x+13=0⇒b2-4ac=49-4(1)(13)=49-52=-3<0Since,…

Q: Find all complex solutions x4-3x2=28

A: Given equation

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

A: Given: 2x2+x-2=0 Solve the equation for x, using the equation. x=-b±b2-4ac2a here, a=2, b=1 and…

Q: Use Descartes’ rule of signs to determine the number of possible positive, negative, and nonreal…

A: Given equation is, 3x3-4x2+3x+7=0 Arranging the equation in standard form and counting the change in…

Q: Find the complex solutions x5÷2+8x3÷2+25x1÷2=0

A:

Q: first use the discriminant to determine whether the equation has two nonreal complex solutions, one…

A:

Q: What are the complex solutions for r2- 6x +34? 土

A:

Q: What are the roots of the equation 4x² = 5x – 3 in simplest a + bi form?

A: Given : 4x2 = 5x-3