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Magazine Problem 79
Simplify each expression to \(i, 1,-i,\) or \(-1\) $$i^{-6}$$
Problem 80
Simplify each expression to \(i, 1,-i,\) or \(-1\) $$i^{-15}$$
Problem 80
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. $$x^{2}+y^{2}-10 x+8 y+5=0$$
Problem 81
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. $$x^{2}+y^{2}+12 x-4 y+29=0$$
Problem 81
Simplify each expression to \(i, 1,-i,\) or \(-1\) $$\frac{1}{i^{9}}$$
Problem 81
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 $$2 i,-2 i$$
Problem 82
Simplify each expression to \(i, 1,-i,\) or \(-1\) $$\frac{1}{i^{12}}$$
Problem 82
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 $$1+\sqrt{3}, 1-\sqrt{3}$$
Problem 82
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. $$x^{2}+y^{2}-10 x+6 y+21=0$$
Problem 83
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. $$x^{2}+y^{2}+4 x-5=0$$
