If c^2 = d^2, which of the following must be true?  Select the correct option:
A) c = d
B) |c| = |d|
C) c = |d|
D) c = −|d|
E) c=-d
Since c^2=d^2 we have 0=c^2 – d^2 =(c-d)*(c+d). So c=d or c=-d.   So only (A) and only (E) cannot be an answer.   The choice (C) tells us that k should be greater than or equal to 0.   Similarly the choice (D) tells us that k should be less than or equal to 0.   So neither (C) nor (D) cannot be the answer.   The answer is, therefore, (|c| = |d|).
<result>B</result>
If c^2 = d^2, which of the following must be true?