Chapter 3

Multiply as indicated. Write each product in standand form. $$i(2+7 i)(2-7 i)$$

Solve each quadratic equation by completing the square. $$2 x(2 x-5)=2$$

Find the center-radius form of the equation of a circle with the given center and radius. Graph the circle. Center \((0,0),\) radius 2

Multiply as indicated. Write each product in standand form. $$3 i(2-i)^{2}$$

Find the center-radius form of the equation of a circle with the given center and radius. Graph the circle. Center \((0,0),\) radius 4

Multiply as indicated. Write each product in standand form. $$-5 i(4-3 i)^{2}$$

Evaluate the discriminant, and use it to determine the number of real solutions of the equation. If the equation does have real solutions, tell whether they are rational or irrational. Do not actually solve the equation. $$x^{2}+8 x+16=0$$

Find the center-radius form of the equation of a circle with the given center and radius. Graph the circle. Center \((1,-2),\) radius 4

Multiply as indicated. Write each product in standand form. $$(2+i)(2-i)(4+3 i)$$

Evaluate the discriminant, and use it to determine the number of real solutions of the equation. If the equation does have real solutions, tell whether they are rational or irrational. Do not actually solve the equation. $$8 x^{2}=14 x-3$$

Multiply as indicated. Write each product in standand form. $$(3-i)(3+i)(2-6 i)$$

Evaluate the discriminant, and use it to determine the number of real solutions of the equation. If the equation does have real solutions, tell whether they are rational or irrational. Do not actually solve the equation. $$4 x^{2}=6 x+3$$

Find the center-radius form of the equation of a circle with the given center and radius. Graph the circle. Center \((-2,0),\) radius 5

Simplify each expression to \(i, 1,-i,\) or \(-1\) $$i^{5}$$

Evaluate the discriminant, and use it to determine the number of real solutions of the equation. If the equation does have real solutions, tell whether they are rational or irrational. Do not actually solve the equation. $$2 x^{2}-4 x+1=0$$

Find the center-radius form of the equation of a circle with the given center and radius. Graph the circle. Center \((-3,0),\) radius 2

Simplify each expression to \(i, 1,-i,\) or \(-1\) $$i^{8}$$

Evaluate the discriminant, and use it to determine the number of real solutions of the equation. If the equation does have real solutions, tell whether they are rational or irrational. Do not actually solve the equation. $$9 x^{2}+11 x+4=0$$

Find the center-radius form of the equation of a circle with the given center and radius. Graph the circle. Center \((0,4),\) radius \(\sqrt{6}\)

Simplify each expression to \(i, 1,-i,\) or \(-1\) $$i^{15}$$

Evaluate the discriminant, and use it to determine the number of real solutions of the equation. If the equation does have real solutions, tell whether they are rational or irrational. Do not actually solve the equation. $$3 x^{2}=4 x-5$$

Find the center-radius form of the equation of a circle with the given center and radius. Graph the circle. Center \((0,-3),\) radius \(\sqrt{7}\)

Simplify each expression to \(i, 1,-i,\) or \(-1\) $$i^{19}$$

For each pair of numbers, find the values of \(a, b,\) and \(c\) for which the quadratic equation ax \(^{2}+b x+c=0\) has the given numbers as solutions. Answers may vary. (Hint: Use the zero-product property in reverses $$4,5$$

Find the center-radius form of the circle with the given equation. Determine the coordinates of the center, find the radius, and graph the circle. $$x^{2}+y^{2}+2 x+2 y-23=0$$

Simplify each expression to \(i, 1,-i,\) or \(-1\) $$i^{64}$$

For each pair of numbers, find the values of \(a, b,\) and \(c\) for which the quadratic equation ax \(^{2}+b x+c=0\) has the given numbers as solutions. Answers may vary. (Hint: Use the zero-product property in reverses $$-3,2$$

Simplify each expression to \(i, 1,-i,\) or \(-1\) $$i^{102}$$

For each pair of numbers, find the values of \(a, b,\) and \(c\) for which the quadratic equation ax \(^{2}+b x+c=0\) has the given numbers as solutions. Answers may vary. (Hint: Use the zero-product property in reverses $$1+\sqrt{2}, 1-\sqrt{2}$$

Find the center-radius form of the circle with the given equation. Determine the coordinates of the center, find the radius, and graph the circle. $$x^{2}+y^{2}+6 x-6 y+2=0$$

Simplify each expression to \(i, 1,-i,\) or \(-1\) $$i^{-6}$$

Find the center-radius form of the circle with the given equation. Determine the coordinates of the center, find the radius, and graph the circle. $$x^{2}+y^{2}-10 x+8 y+5=0$$

Simplify each expression to \(i, 1,-i,\) or \(-1\) $$i^{-15}$$

For each pair of numbers, find the values of \(a, b,\) and \(c\) for which the quadratic equation ax \(^{2}+b x+c=0\) has the given numbers as solutions. Answers may vary. (Hint: Use the zero-product property in reverses $$2 i,-2 i$$

Find the center-radius form of the circle with the given equation. Determine the coordinates of the center, find the radius, and graph the circle. $$x^{2}+y^{2}+12 x-4 y+29=0$$

Simplify each expression to \(i, 1,-i,\) or \(-1\) $$\frac{1}{i^{9}}$$

For each pair of numbers, find the values of \(a, b,\) and \(c\) for which the quadratic equation ax \(^{2}+b x+c=0\) has the given numbers as solutions. Answers may vary. (Hint: Use the zero-product property in reverses $$1+\sqrt{3}, 1-\sqrt{3}$$

Find the center-radius form of the circle with the given equation. Determine the coordinates of the center, find the radius, and graph the circle. $$x^{2}+y^{2}-10 x+6 y+21=0$$

Simplify each expression to \(i, 1,-i,\) or \(-1\) $$\frac{1}{i^{12}}$$

For each pair of numbers, find the values of \(a, b,\) and \(c\) for which the quadratic equation ax \(^{2}+b x+c=0\) has the given numbers as solutions. Answers may vary. (Hint: Use the zero-product property in reverses $$2-\sqrt{5}, 2+\sqrt{5}$$

Find the center-radius form of the circle with the given equation. Determine the coordinates of the center, find the radius, and graph the circle. $$x^{2}+y^{2}+4 x-5=0$$

Simplify each expression to \(i, 1,-i,\) or \(-1\) $$\frac{1}{i^{-51}}$$

For each pair of numbers, find the values of \(a, b,\) and \(c\) for which the quadratic equation ax \(^{2}+b x+c=0\) has the given numbers as solutions. Answers may vary. (Hint: Use the zero-product property in reverses $$3 i,-3 i$$

Find the center-radius form of the circle with the given equation. Determine the coordinates of the center, find the radius, and graph the circle. $$x^{2}+y^{2}-2 y-3=0$$

Simplify each expression to \(i, 1,-i,\) or \(-1\) $$\frac{1}{i^{-46}}$$

Simplify each expression to \(i, 1,-i,\) or \(-1\) $$\frac{-1}{-i^{12}}$$

Sketch a graph of \(f(x)=a x^{2}+b x+c\) that satisfies each set of conditions. $$a>0, b^{2}-4 a c<0$$

Simplify each expression to \(i, 1,-i,\) or \(-1\) $$\frac{-1}{-i^{15}}$$

Sketch a graph of \(f(x)=a x^{2}+b x+c\) that satisfies each set of conditions. $$a<0, b^{2}-4 a c<0$$

Simplify each expression to \(i, 1,-i,\) or \(-1\) $$\frac{(-1)^{4}}{i^{-16}}$$