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Chapter 1: Problem 20
Let \(x\) represent the number. Use the given conditions to write an equation. Solve the equation and find the number. Five more than four times a number is that number increased by \(35 .\) Find the number.
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Explain how to add complex numbers. Provide an example with your explanation.
Which one of the following is true? a. Some irrational numbers are not complex numbers. b. \((3+7 i)(3-7 i)\) is an imaginary number. c. \(\frac{7+3 i}{5+3 i}=\frac{7}{5}\) d. In the complex number system, \(x^{2}+y^{2}\) (the sum of two squares) can be factored as \((x+y i)(x-y i)\)
In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$\frac{-15-\sqrt{-18}}{33}$$
In Exercises \(73-74\), use the method for solving quadratic inequalities to solve each higher-order polynomial inequality. $$ x^{3}+x^{2}-4 x-4>0 $$
In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$(3 \sqrt{-7})(2 \sqrt{-8})$$
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