Question

Drag each expression to the correct location on the table. Determine which expressions represent real numbers and which expressions represent complex numbers.

a. −12
b. √1−5
c.6
d. 16

Answer 1

Expressions a, c, and d (−12, 6, and 16) are real numbers because they are integers. Expression b (∙1−5) represents a complex number because it involves the square root of a negative number, which requires the imaginary unit to express.

Step-by-step explanation:

The question involves determining whether each expression represents a real number or a complex number. A real number can be any value on the number line, including integers, fractions, and irrational numbers, while a complex number includes an imaginary unit i, where i is the square root of -1. For the given expressions:

• −12 is a real number because it is an integer.
• ∙1−5 suggests taking the square root of a negative number, which is not a real number but a complex one. Hence, ∙1−5 (sqrt(-4)) is equal to 2i, which is a complex number.
• 6 is a real number because it is an integer.
• 16 is a real number because it is an integer.

Therefore, expressions a, c, and d represent real numbers while expression b represents a complex number.