Chapter 1

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (5-2 i)+(-3+6 i) $$

Exer. 1-10: Express the number in the form \(a / b\), where \(a\) and \(b\) are integers. $$ \left(-\frac{2}{3}\right)^{4} $$

Express as a polynomial. $$ \left(3 x^{3}+4 x^{2}-7 x+1\right)+\left(9 x^{3}-4 x^{2}-6 x\right) $$

Exer. 1-2: If \(x<0\) and \(y>0\), determine the sign of the real number. (a) \(x y\) (b) \(x^{2} y\) (c) \(\frac{x}{y}+x\) (d) \(y-x\)

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (-5+7 i)+(4+9 i) $$

Exer. 1-10: Express the number in the form \(a / b\), where \(a\) and \(b\) are integers. $$ (-3)^{3} $$

Express as a polynomial. $$ \left(7 x^{3}+2 x^{2}-11 x\right)+\left(-3 x^{3}-2 x^{2}+5 x-3\right) $$

Exer. 1-2: If \(x<0\) and \(y>0\), determine the sign of the real number. (a) \(\frac{x}{y}\) (b) \(x y^{2}\) (c) \(\frac{x-y}{x y}\) (d) \(y(y-x)\)

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (7-6 i)-(-11-3 i) $$

Exer. 1-10: Express the number in the form \(a / b\), where \(a\) and \(b\) are integers. $$ \frac{2^{-3}}{3^{-2}} $$

Express as a polynomial. $$ \left(4 x^{3}+5 x-3\right)-\left(3 x^{3}+2 x^{2}+5 x-7\right) $$

Exer. 3-6: Replace the symbol \(\square\) with either \(<,>\), or \(=\) to make the resulting statement true. (a) \(-7 \square-4\) (b) \(\frac{\pi}{2} \square 1.57\) (c) \(\sqrt{225} \square 15\)

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (-3+8 i)-(2+3 i) $$

Exer. 1-10: Express the number in the form \(a / b\), where \(a\) and \(b\) are integers. $$ \frac{2^{0}+0^{2}}{2+0} $$

Express as a polynomial. $$ \left(6 x^{3}-2 x^{2}+x-2\right)-\left(8 x^{2}-x-2\right) $$

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (3+5 i)(2-7 i) $$

Exer. 1-10: Express the number in the form \(a / b\), where \(a\) and \(b\) are integers. $$ -2^{4}+3^{-1} $$

Express as a polynomial. $$ (2 x+5)(3 x-7) $$

Exer. 3-6: Replace the symbol \(\square\) with either \(<,>\), or \(=\) to make the resulting statement true. (a) \(\frac{1}{11} \square 0.09\) (b) \(\frac{2}{3} \square 0.6666\) (c) \(\frac{22}{7} \square \pi\)

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (-2+6 i)(8-i) $$

Exer. 1-10: Express the number in the form \(a / b\), where \(a\) and \(b\) are integers. $$ \left(-\frac{3}{2}\right)^{4}-2^{-4} $$

Express as a polynomial. $$ (3 x-4)(2 x+9) $$

Exer. 3-6: Replace the symbol \(\square\) with either \(<,>\), or \(=\) to make the resulting statement true. (a) \(\frac{1}{7} \square 0.143\) (b) \(\frac{5}{6} \square 0.833\) (c) \(\sqrt{2} \square 1.4\)

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (1-3 i)(2+5 i) $$

Exer. 1-10: Express the number in the form \(a / b\), where \(a\) and \(b\) are integers. $$ 16^{-3 / 4} $$

Express as a polynomial. $$ (5 x+7 y)(3 x+2 y) $$

Exer. 7-8: Express the statement as an inequality. (a) \(x\) is negative. (b) \(y\) is nonnegative. (c) \(q\) is less than or equal to \(\pi\). (d) \(d\) is between 4 and 2 . (e) \(t\) is not less than 5 . (f) The negative of \(z\) is not greater than 3 . (g) The quotient of \(p\) and \(q\) is at most 7 . (h) The reciprocal of \(w\) is at least \(9 .\) (i) The absolute value of \(x\) is greater than 7 .

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (8+2 i)(7-3 i) $$

Exer. 1-10: Express the number in the form \(a / b\), where \(a\) and \(b\) are integers. $$ 9^{5 / 2} $$

Express as a polynomial. $$ (4 x-3 y)(x-5 y) $$

Exer. 7-8: Express the statement as an inequality. (a) \(b\) is positive. (b) \(s\) is nonpositive. (c) \(w\) is greater than or equal to \(-4\). (d) \(c\) is between \(\frac{1}{3}\) and \(\frac{1}{3}\). (e) \(p\) is not greater than \(-2\). (f) The negative of \(m\) is not less than \(-2\). (g) The quotient of \(r\) and \(s\) is at least \(\frac{1}{3}\). (h) The reciprocal of \(f\) is at most 14 . (i) The absolute value of \(x\) is less than 4 .

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (5-2 i)^{2} $$

Exer. 91-92: In evaluating negative numbers raised to fractional powers, it may be necessary to evaluate the root and integer power separately. For example, \((-3)^{2 / 5}\) can be evaluated successfully as \(\left[(-3)^{1 / 5}\right]^{2}\) or \(\left[(-3)^{2}\right]^{1 / 5}\), whereas an error message might otherwise appear. Approximate the realnumber expression to four decimal places. (a) \((-3)^{2 / 5}\) (b) \((-5)^{4 / 3}\)

Exer. 1-10: Express the number in the form \(a / b\), where \(a\) and \(b\) are integers. $$ (-0.008)^{2 / 3} $$

Express as a polynomial. $$ (2 u+3)(u-4)+4 u(u-2) $$

Exer. 9-14: Rewrite the number without using the absolute value symbol, and simplify the result. (a) \(|-3-2|\) (b) \(|-5|-|2|\) (c) \(|7|+|-4|\)

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (6+7 i)^{2} $$

Express as a polynomial. $$ (3 u-1)(u+2)+7 u(u+1) $$

Exer. 1-10: Express the number in the form \(a / b\), where \(a\) and \(b\) are integers. $$ (0.008)^{-2 / 3} $$

Exer. 9-14: Rewrite the number without using the absolute value symbol, and simplify the result. (a) \(|-11+1|\) (b) \(|6|-|-3|\) (c) \(|8|+|-9|\)

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ i(3+4 i)^{2} $$

Express as a polynomial. $$ (3 x+5)\left(2 x^{2}+9 x-5\right) $$

Exer. 11-46: Simplify. $$ \left(\frac{1}{2} x^{4}\right)\left(16 x^{5}\right) $$

Exer. 9-14: Rewrite the number without using the absolute value symbol, and simplify the result. (a) \((-5)|3-6|\) (b) \(|-6| /(-2)\) (c) \(|-7|+|4|\)

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ i(2-7 i)^{2} $$

Express as a polynomial. $$ (7 x-4)\left(x^{3}-x^{2}+6\right) $$

Exer. 11-46: Simplify. $$ \left(-3 x^{-2}\right)\left(4 x^{4}\right) $$

Exer. 9-14: Rewrite the number without using the absolute value symbol, and simplify the result. (a) \((4)|6-7|\) (b) \(5 /|-2|\) (c) \(|-1|+|-9|\)

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (3+4 i)(3-4 i) $$

Express as a polynomial. $$ \left(t^{2}+2 t-5\right)\left(3 t^{2}-t+2\right) $$