Geometry and HappyCal / Mr. Hansen 5/25/2010

Name: _________________________

Field Trip Substitute Worksheet
(This is a required assignment for students in Forms III, IV, and V who missed both
the May 14 field trip and the May 25 field trip. Form VI students are exempt.)

1.

The following is an erroneous proof that Circle the step in which the error appears, and explain clearly (in complete sentences) why the step is illegal. There is only one error. Consider the expression By the distributive property, this equation is true: . For convenience, let x = 5.33. Then our equation becomes . . .

2.

The following is an erroneous proof that −1 = 1. Circle the step in which the error appears, and explain clearly (in complete sentences) why the step is illegal. There is only one error. Incidentally, the error is not the use of the radical sign with −1. In the complex number system, −1 has two square roots, and the principal one is denoted , just as the principal square root of the real number 49 is denoted Moreover, just as 49 has two square roots, namely 7 and −7, −1 has two square roots, namely i and −i. Remember, however, that the radical symbol always refers to the principal square root. If we want the negative square root, we have to indicate it explicitly. For example, . Similarly, . Here is the erroneous proof: (Q.E.D.)