1985 AHSME Problems/Problem 23
Problem
If 
and 
, where 
, then which of the following is not correct?
Solution 1
Notice that 
and 
. We have 
.
We also have 
.
Finally, 
.
Let 
. We have
.
For 
, so
.
Therefore, for 
, and
, so 
.
As a check, we have 
for 
, and
.
Finally, for 
we have 
, and
, and this is true for all other answer choices.
Solution 2 (using polar complex numbers)
Note that 
and that 
.
Then 
and 
.
Thus, 
. Testing 
for choices A, B, C, D, and E, respectively, we find that for 
, 
. The answer is 
.
See Also
| 1985 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 22 |
Followed by Problem 24 | |
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