Algebra and Trigonometry, 5th Edition

Mid-Chapter Mixed Review

Determine whether the statement is true or false.

1. The product of a complex number and its conjugate is a real number. [3.1]

2. Every quadratic equation has at least one x-intercept. [3.2]

3. If a quadratic equation has two different real-number solutions, then its discriminant is positive. [3.2]

4. The vertex of the graph of the function $f(x)=3{(x+4)}^2+5$ is (4, 5). [3.3]

Express the number in terms of i. [3.1]

5. $\sqrt{-36}$

6. $\sqrt{-5}$

7. $-\sqrt{-16}$

8. $\sqrt{-32}$

Simplify. Write answers in the form $a+bi$, where a and b are real numbers. [3.1]

9. $(3-2i)+(-4+3i)$

10. $(-5+i)-(2-4i)$

11. $(2+3i)(4-5i)$

12. $\frac{3+i}{-2+5i}$

Simplify. [3.1]

13. $i^{13}$

14. $i^{44}$

15. ${(-i)}^5$

16. ${(2i)}^6$

Solve. [3.2]

17. $x^2+3x-4=0$

18. $2x^2+6=-7x$

19. $4x^2=24$

20. $x^2+100=0$

21. Find the zeros of $f(x)=4x^2-8x-3$ by completing the square. Show ...