Lesson 8 I May Be Irrational, But You’re Imaginary Solidify Understanding

Ready

Classify each of the numbers represented below according to the sets to which they belong. If a number fits in more than one set, then select all that apply.

1.

$π$

A.

whole numbers $(W)$

B.

integers $(Z)$

C.

rational numbers $(Q)$

D.

irrational numbers $(\overset{―}{Q})$

E.

real numbers $(R)$

2.

$- 13$

A.

whole numbers $(W)$

B.

integers $(Z)$

C.

rational numbers $(Q)$

D.

irrational numbers $(\overset{―}{Q})$

E.

real numbers $(R)$

3.

$\sqrt{625}$

A.

whole numbers $(W)$

B.

integers $(Z)$

C.

rational numbers $(Q)$

D.

irrational numbers $(\overset{―}{Q})$

E.

real numbers $(R)$

4.

$0$

A.

whole numbers $(W)$

B.

integers $(Z)$

C.

rational numbers $(Q)$

D.

irrational numbers $(\overset{―}{Q})$

E.

real numbers $(R)$

5.

$\sqrt{75}$

A.

whole numbers $(W)$

B.

integers $(Z)$

C.

rational numbers $(Q)$

D.

irrational numbers $(\overset{―}{Q})$

E.

real numbers $(R)$

6.

$\frac{9}{3}$

A.

whole numbers $(W)$

B.

integers $(Z)$

C.

rational numbers $(Q)$

D.

irrational numbers $(\overset{―}{Q})$

E.

real numbers $(R)$

7.

$\sqrt{\frac{4}{9}}$

A.

whole numbers $(W)$

B.

integers $(Z)$

C.

rational numbers $(Q)$

D.

irrational numbers $(\overset{―}{Q})$

E.

real numbers $(R)$

8.

$5 + \sqrt{2}$

A.

whole numbers $(W)$

B.

integers $(Z)$

C.

rational numbers $(Q)$

D.

irrational numbers $(\overset{―}{Q})$

E.

real numbers $(R)$

9.

$- 13 + \sqrt{121}$

A.

whole numbers $(W)$

B.

integers $(Z)$

C.

rational numbers $(Q)$

D.

irrational numbers $(\overset{―}{Q})$

E.

real numbers $(R)$

Set

Perform the indicated operations.

10.

$3 + \sqrt{2} - 7 + 3 \sqrt{2}$

11.

$\sqrt{5} - 9 + 8 \sqrt{5} + 11 - \sqrt{5}$

12.

$\sqrt{12} + \sqrt{48}$

13.

$\sqrt{8} - \sqrt{18} + \sqrt{32}$

14.

${(- 11 i)}^{2}$

15.

${(\sqrt{7} \cdot i)}^{2}$

16.

$(21 + 4 i) + (9 + 8 i)$

17.

$(6 + 10 i) - (2 + 5 i)$

18.

$(- 18 - 3 i) + (18 + 2 i)$

19.

$(7 + 13 i) + (7 - 13 i)$

Multiply.

20.

$(2 + 5 i) (3 + 2 i)$

21.

$(6 - 8 i) (1 - 2 i)$

22.

$(7 + 3 i) (3 - i)$

23.

$(10 + 3 i) (10 - 3 i)$

24.

In problem 19, you added two complex numbers that were conjugates. When you add two conjugates, will your answer become a real number? Justify your answer.

25.

In problem 23, you multiplied two complex numbers that were conjugates. When you multiply two conjugates, will your answer become a real number? Justify your answer.

Go

Solve.

26.

$m^{2} + 15 m + 56 = 0$

27.

$5 x^{2} - 3 x + 7 = 0$

28.

$x^{2} - 10 x + 21 = 0$

29.

$6 x^{2} + 7 x - 5 = 0$

30.

$x^{2} + 4 = 0$

31.

$x^{2} + 18 = 0$