Chapter 1

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (-3+\sqrt{-25})(8-\sqrt{-36}) $$

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

Exer. 11-46: Simplify. $$ \left(-2 r^{2} s\right)^{5}\left(3 r^{-1} s^{3}\right)^{2} $$

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ \frac{4+\sqrt{-81}}{7-\sqrt{-64}} $$

Express as a polynomial. $$ (x+2)^{2}(x-2)^{2} $$

Exer. 11-46: Simplify. $$ \left(\frac{3 x^{5} y^{4}}{x^{0} y^{-3}}\right)^{2} $$

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ \frac{5-\sqrt{-121}}{1+\sqrt{-25}} $$

Express as a polynomial. $$ (x+y)^{2}(x-y)^{2} $$

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

Exer. 25-32: Rewrite the expression without using the absolute value symbol, and simplify the result. $$ \left|-x^{2}-1\right| $$

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ \frac{\sqrt{-36} \sqrt{-49}}{\sqrt{-16}} $$

Express as a polynomial. $$ (\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y}) $$

Exer. 11-46: Simplify. $$ \left(4 a^{3 / 2}\right)\left(2 a^{1 / 2}\right) $$

Exer. 33-40: Replace the symbol \(\square\) with either \(=\) or \(\neq\) to make the resulting statement true for all real numbers \(a, b\), \(c\), and \(d\), whenever the expressions are defined. $$ \frac{a b+a c}{a} \square b+a c $$

Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ \frac{\sqrt{-25}}{\sqrt{-16} \sqrt{-81}} $$

Express as a polynomial. $$ (\sqrt{x}+\sqrt{y})^{2}(\sqrt{x}-\sqrt{y})^{2} $$

Exer. 11-46: Simplify. $$ \left(-6 x^{7 / 5}\right)\left(2 x^{8 / 5}\right) $$

Exer. 33-40: Replace the symbol \(\square\) with either \(=\) or \(\neq\) to make the resulting statement true for all real numbers \(a, b\), \(c\), and \(d\), whenever the expressions are defined. $$ \frac{a b+a c}{a} \square b+c $$

Find the values of \(x\) and \(y\), where \(x\) and \(y\) are $$ 4+(x+2 y) i=x+2 i $$

Express as a polynomial. $$ \left(x^{1 / 3}-y^{1 / 3}\right)\left(x^{2 / 3}+x^{1 / 3} y^{1 / 3}+y^{2 / 3}\right) $$

Exer. 11-46: Simplify. $$ \left(3 x^{5 / 6}\right)\left(8 x^{2 / 3}\right) $$

Find the values of \(x\) and \(y\), where \(x\) and \(y\) are $$ (x-y)+3 i=7+y i $$

Express as a polynomial. $$ \left(x^{1 / 3}+y^{1 / 3}\right)\left(x^{2 / 3}-x^{1 / 3} y^{1 / 3}+y^{2 / 3}\right) $$

Exer. 11-46: Simplify. $$ (8 r)^{1 / 3}\left(2 r^{1 / 2}\right) $$

Find the values of \(x\) and \(y\), where \(x\) and \(y\) are $$ (2 x-y)-16 i=10+4 y i $$

Express as a polynomial. $$ (x-2 y)^{3} $$

Exer. 11-46: Simplify. $$ \left(27 a^{6}\right)^{-2 / 3} $$

Exer. 33-40: Replace the symbol \(\square\) with either \(=\) or \(\neq\) to make the resulting statement true for all real numbers \(a, b\), \(c\), and \(d\), whenever the expressions are defined. $$ (a \div b) \div c \square a \div(b \div c) $$

Find the values of \(x\) and \(y\), where \(x\) and \(y\) are $$ 8+(3 x+y) i=2 x-4 i $$

Express as a polynomial. $$ (x+3 y)^{3} $$

Exer. 11-46: Simplify. $$ \left(25 z^{4}\right)^{-3 / 2} $$

Exer. 33-40: Replace the symbol \(\square\) with either \(=\) or \(\neq\) to make the resulting statement true for all real numbers \(a, b\), \(c\), and \(d\), whenever the expressions are defined. $$ (a-b)-c \square a-(b-c) $$

Find the solutions of the equation $$ x^{2}-6 x+13=0 $$

Express as a polynomial. $$ (2 x+3 y)^{3} $$

Exer. 11-46: Simplify. $$ \left(8 x^{-2 / 3}\right) x^{1 / 6} $$

Exer. 33-40: Replace the symbol \(\square\) with either \(=\) or \(\neq\) to make the resulting statement true for all real numbers \(a, b\), \(c\), and \(d\), whenever the expressions are defined. $$ \frac{a-b}{b-a} \square-1 $$