Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1 - 4, add or subtract, and simplify. (2x + 3) + (-x + 6)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1 - 4, add or subtract, and simplify. (3y - x) + (2x - y)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1 - 4, add or subtract, and simplify. (2a + 4d) - (a + 2d)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1 - 4, add or subtract, and simplify. (6z - 1) - (z + 3)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5 - 10, multiply and simplify. (x - 3)(x + 2)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5 - 10, multiply and simplify. (2x - 1)(x + 3)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5 - 10, multiply and simplify. \((x-\sqrt{2})(x+\sqrt{2})\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5 - 10, multiply and simplify. \((x+2 \sqrt{3})(x-2 \sqrt{3})\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5 - 10, multiply and simplify. \([x-(1+\sqrt{2})][x-(1-\sqrt{2})]\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5 - 10, multiply and simplify. \([x-(2+\sqrt{3})][x-(2-\sqrt{3})]\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 18, write the sum or difference in the standard form a + bi without using a calculator. (2 - 3i) + (6 + 5i)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 18, write the sum or difference in the standard form a + bi without using a calculator. (2 - 3i) + (3 - 4i)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 18, write the sum or difference in the standard form a + bi without using a calculator. (7 - 3i) + (6 - i)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 18, write the sum or difference in the standard form a + bi without using a calculator. (2 + i) - (9i - 3)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 18, write the sum or difference in the standard form a + bi without using a calculator. \((2-i)+(3-\sqrt{-3})\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 18, write the sum or difference in the standard form a + bi without using a calculator. \((\sqrt{5}-3 i)+(-2+\sqrt{-9})\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 18, write the sum or difference in the standard form a + bi without using a calculator. \(\left(i^{2}+3\right)-\left(7+i^{3}\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 18, write the sum or difference in the standard form a + bi without using a calculator. \(\left(\sqrt{7}+i^{2}\right)-(6-\sqrt{-81})\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 - 16, write the product in standard form without using a calculator. (2 + 3i)(2 - i)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 - 16, write the product in standard form without using a calculator. (2 - i)(1 + 3i)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 - 16, write the product in standard form without using a calculator. (1 - 4i)(3 - 2i)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 - 16, write the product in standard form without using a calculator. (5i - 3)(2i + 1)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 - 16, write the product in standard form without using a calculator. (7i - 3)(2 + 6i)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 - 16, write the product in standard form without using a calculator. \((\sqrt{-4}+i)(6-5 i)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 - 16, write the product in standard form without using a calculator. (-3 - 4i)(1 + 2i)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 - 16, write the product in standard form without using a calculator. \((\sqrt{-2}+2 i)(6+5 i)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, write the expression in the form bi, where b is a real number. \(\sqrt{-16}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, write the expression in the form bi, where b is a real number. \(\sqrt{-25}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, write the expression in the form bi, where b is a real number. \(\sqrt{-3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, write the expression in the form bi, where b is a real number. \(\sqrt{-5}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, find the real numbers x and y that make the equation true. 2 + 3i = x + yi

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, find the real numbers x and y that make the equation true. 3 + yi = x - 7i

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, find the real numbers x and y that make the equation true. (5 - 2i) - 7 = x - (3 + yi)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, find the real numbers x and y that make the equation true. (x + 6i) = (3 - i) + (4 - 2yi)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2528, write the complex number in standard form. \((3+2 i)^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2528, write the complex number in standard form. \((1-i)^{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2528, write the complex number in standard form. \(\left(\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2} i\right)^{4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2528, write the complex number in standard form. \(\left(\frac{\sqrt{3}}{2}+\frac{1}{2} i\right)^{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2932, find the product of the complex number and its conjugate. 2 - 3i

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2932, find the product of the complex number and its conjugate. 5 - 6i

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2932, find the product of the complex number and its conjugate. -3 + 4i

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2932, find the product of the complex number and its conjugate. -1-\sqrt{2} i

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3340, write the expression in standard form without using a calculator. \(\frac{1}{2+i}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3340, write the expression in standard form without using a calculator. \(\frac{i}{2-i}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3340, write the expression in standard form without using a calculator. \(\frac{2+i}{2-i}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3340, write the expression in standard form without using a calculator. \(\frac{2+i}{3 i}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3340, write the expression in standard form without using a calculator. \(\frac{(2+i)^{2}(-i)}{1+i}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3340, write the expression in standard form without using a calculator. \(\frac{(2-i)(1+2 i)}{5+2 i}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3340, write the expression in standard form without using a calculator. \(\frac{(1-i)(2-i)}{1-2 i}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3340, write the expression in standard form without using a calculator. \(\frac{(1-\sqrt{2} i)(1+i)}{(1+\sqrt{2} i)}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4144, solve the equation. \(x^{2}+2 x+5=0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4144, solve the equation. \(3 x^{2}+x+2=0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4144, solve the equation. \(4 x^{2}-6 x+5=x+1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4144, solve the equation. \(x^{2}+x+11=5 x-8\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False There are no complex numbers z satisfying \(z=-\bar{z}\). Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False For the complex number \(i, i+i^{2}+i^{3}+i^{4}=0\). Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4750, solve the problem without using a calculator. Multiple Choice Which of the following is the standard form for the product (2 + 3i)(2 - 3i)? (A) -5 + 12i (B) 4 - 9i (C) 13 - 3i (D) -5 (E) 13 + 0i

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4750, solve the problem without using a calculator. Multiple Choice Which of the following is the standard form for the quotient \(\frac{1}{i}\)? (A) 1 (B) -1 (C) i (D) -1/i (E) 0 - i

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4750, solve the problem without using a calculator. Multiple Choice Assume that 2 - 3i is a solution of \(a x^{2}+b x+c=0\), where a, b, c are real numbers. Which of the following is also a solution of the equation? (A) 2 + 3i (B) -2 - 3i

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4750, solve the problem without using a calculator. Multiple Choice Which of the following is the standard form for the power \((1-i)^{3}\)? (A) -4i (B) -2 + 2i (C) -2 - 2i (D) 2 + 2i (E) 2 - 2i

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activity The Powers of i (a) Simplify the complex numbers \(i, i^{2}, \ldots, i^{8}\) by evaluating each one. (b) Simplify the complex numbers \(i^{-1}, i^{-2}, \ldots, i^{-8}\) by evaluating each one. (c) Evaluate \(i^{0}\). (d) Writing to Learn Discuss your results from (a

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Describe the nature of the graph of \(f(x)=a x^{2}+b x+c\) when a, b, and c are real numbers and the equation \(a x^{2}+b x+c=0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Prove that the difference between a complex number and its conjugate is a complex number whose real part is 0.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Prove that the product of a complex number and its complex conjugate is a complex number whose imaginary part is zero.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Prove that the complex conjugate of a product of two complex numbers is the product of their complex conjugates.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Prove that the complex conjugate of a sum of two complex numbers is the sum of their complex conjugates.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Explain why -i is a solution of \(x^{2}-\text { ix }+2=0\) but i is not.