In this problem, the square root is a function from the complex numbers to the complex numbers.
If and are non-zero numbers such that , which of the following is always true?
(A)
(B)
(C)
(D)
(E)
Calvin has a collection of special weighted dice that all share special properties:
Let be the maximum number of dice in the collection and let be the sum of all the faces of all the dice in the maximum collection size.
Find .
I claim that using the proof below but I was just told that I might have just committed a small mistake.
A.
B.
C.
D.
E.
F.
G.
H.
I.
Where did I go wrong? At which step(s) did I commit a fallacy?
Note: .
What is the wrong step in the following proof that ?
Let be a complex number such that .
Solving this equation gives .
Since for our previously mentioned values of , cube rooting both sides gives .
Subtracting from both sides gives .