1. Complex Numbers

2. The equation x2 + 1 = 0 has no real number solutions since any solution must be a number whose square is -1.

3. The equation x2 + 1 = 0 has no real number solutions since any solution must be a number whose square is -1.

4. The equation x2 + 1 = 0 has no real number solutions since any solution must be a number whose square is -1.

5. The equation x2 + 1 = 0 has no real number solutions since any solution must be a number whose square is -1.

6. The equation x2 + 1 = 0 has no real number solutions since any solution must be a number whose square is -1.

7. In the set of real numbers,
all squares are nonnegative numbers because

8. In the set of real numbers,
all squares are nonnegative numbers because

9. In the set of real numbers,
all squares are nonnegative numbers because
the product of any two positive numbers is positive

10. In the set of real numbers,
all squares are nonnegative numbers because
the product of any two positive numbers is positive

11. In the set of real numbers,
all squares are nonnegative numbers because
the product of any two positive numbers is positive
&
the product of any two negative numbers is positive

12. In the set of real numbers,
all squares are nonnegative numbers because
the product of any two positive numbers is positive
&
the product of any two negative numbers is positive

14. So we must define a number i so that

15. So we must define a number i so that

16. For any positive real number b

17. Write the number as a product of a real number and the number i

18. Write the number as a product of a real number and the number i

19. Write the number as a product of a real number and the number i

20. Write the number as a product of a real number and the number i

21. Write the number as a product of a real number and the number i

22. Write the number as a product of a real number and the number i

23. Write the number as a product of a real number and the number i

24. Write the number as a product of a real number and the number i

25. Write the number as a product of a real number and the number i

26. Write the number as a product of a real number and the number i

27. Write the number as a product of a real number and the number i

28. Multiply

29. Multiply

30. Multiply

31. Multiply

32. Multiply

33. Multiply

34. Multiply

35. Multiply

36. Multiply

37. Multiply

38. Multiply

39. Multiply

40. Multiply

41. Multiply

42. Multiply

43. Multiply

44. Divide

45. Divide

46. Divide

47. Divide

48. Divide

49. Divide

50. Divide

51. Divide

52. Divide

53. Divide

54. Divide

55. Add

56. Add

57. Add

58. Add

59. Add

60. Add

61. Add

62. Add

63. Add

64. Add

65. Add

66. Add

67. Add

68. Add

69. Subtract

70. Subtract

71. Subtract

72. Subtract

73. Subtract

74. Subtract

75. Subtract

76. Subtract

77. Subtract

78. Subtract

79. Subtract

80. Subtract

81. Subtract

82. Subtract

83. Subtract

84. Subtract

85. Subtract

86. Subtract

87. Subtract

88. Subtract

89. Subtract

90. Subtract

91. Subtract

92. Subtract

93. Subtract

94. Subtract

95. Subtract

96. Subtract

97. Subtract

98. Multiply

99. Multiply

100. Multiply

101. Multiply

102. Multiply

103. Multiply

104. Multiply

105. Multiply

106. Multiply

107. Multiply

108. Multiply

109. Multiply

110. Multiply

111. Multiply

112. Multiply

113. Multiply

114. Multiply

115. Multiply

116. Multiply

117. Multiply

118. Multiply

119. Multiply

120. Multiply

121. Multiply

122. Multiply

123. Multiply

124. Multiply

125. Multiply

126. Multiply

127. Multiply

128. Multiply

129. Multiply

130. Multiply

131. Multiply

132. Multiply

133. Multiply

134. Multiply

135. Multiply

136. Multiply

137. Multiply

138. Multiply

139. Simplify

140. Simplify

141. Simplify

142. Simplify

143. Simplify

144. Simplify

145. Simplify

146. Simplify

147. Simplify

148. Simplify

170. 7.7 Numbers 1-68