91Ó°ÊÓ

Find a ratio of two integers that represents the given number. $$ 0.5 \overline{16} $$

For Exercises \(119-124,\) factor the expressions over the set of complex numbers. For assistance, consider these examples. \(\cdot\) In Chapter \(\mathrm{R}\) we saw that some expressions factor over the set of integers. For example: \(x^{2}-4=(x+2)(x-2)\). \(\cdot\) Some expressions factor over the set of irrational numbers. For example: \(x^{2}-5=(x+\sqrt{5})(x-\sqrt{5})\). \(\cdot\) To factor an expression such as \(x^{2}+4,\) we need to factor over the set of complex numbers. For example, verify that \(x^{2}+4=(x+2 i)(x-2 i)\). a. \(x^{2}-9\) b. \(x^{2}+9\)

Solve for the indicated variable. \(L I^{2}+R I+\frac{1}{C}=0 \quad\) for \(I\)

For Exercises \(119-124,\) factor the expressions over the set of complex numbers. For assistance, consider these examples. \(\cdot\) In Chapter \(\mathrm{R}\) we saw that some expressions factor over the set of integers. For example: \(x^{2}-4=(x+2)(x-2)\). \(\cdot\) Some expressions factor over the set of irrational numbers. For example: \(x^{2}-5=(x+\sqrt{5})(x-\sqrt{5})\). \(\cdot\) To factor an expression such as \(x^{2}+4,\) we need to factor over the set of complex numbers. For example, verify that \(x^{2}+4=(x+2 i)(x-2 i)\). a. \(x^{2}-100\) b. \(x^{2}+100\)

Solve for the indicated variable. \(A=\pi r^{2}+\pi r s\) for \(r\)

For Exercises \(119-124,\) factor the expressions over the set of complex numbers. For assistance, consider these examples. \(\cdot\) In Chapter \(\mathrm{R}\) we saw that some expressions factor over the set of integers. For example: \(x^{2}-4=(x+2)(x-2)\). \(\cdot\) Some expressions factor over the set of irrational numbers. For example: \(x^{2}-5=(x+\sqrt{5})(x-\sqrt{5})\). \(\cdot\) To factor an expression such as \(x^{2}+4,\) we need to factor over the set of complex numbers. For example, verify that \(x^{2}+4=(x+2 i)(x-2 i)\). a. \(x^{2}-64\) b. \(x^{2}+64\)

Find a ratio of two integers that represents the given number. $$ 0 . \overline{534} $$

For Exercises \(119-124,\) factor the expressions over the set of complex numbers. For assistance, consider these examples. \(\cdot\) In Chapter \(\mathrm{R}\) we saw that some expressions factor over the set of integers. For example: \(x^{2}-4=(x+2)(x-2)\). \(\cdot\) Some expressions factor over the set of irrational numbers. For example: \(x^{2}-5=(x+\sqrt{5})(x-\sqrt{5})\). \(\cdot\) To factor an expression such as \(x^{2}+4,\) we need to factor over the set of complex numbers. For example, verify that \(x^{2}+4=(x+2 i)(x-2 i)\). a. \(x^{2}-25\) b. \(x^{2}+25\)

Explain how the discriminant can be used to determine if the solutions to a quadratic equation are imaginary numbers.

For Exercises \(119-124,\) factor the expressions over the set of complex numbers. For assistance, consider these examples. \(\cdot\) In Chapter \(\mathrm{R}\) we saw that some expressions factor over the set of integers. For example: \(x^{2}-4=(x+2)(x-2)\). \(\cdot\) Some expressions factor over the set of irrational numbers. For example: \(x^{2}-5=(x+\sqrt{5})(x-\sqrt{5})\). \(\cdot\) To factor an expression such as \(x^{2}+4,\) we need to factor over the set of complex numbers. For example, verify that \(x^{2}+4=(x+2 i)(x-2 i)\). a. \(x^{2}-3\) b. \(x^{2}+3\)