2007 AIME I Problems/Problem 3
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Problem
The complex number 
is equal to 
, where 
is a positive real number and 
. Given that the imaginary parts of 
and 
are the same, what is equal to?
Solution
Squaring, we find that 
. Cubing and ignoring the real parts of the result, we find that 
.
Setting these two equal, we get that 
, so 
and 
. Since 
, the solution is 
.
See also
| 2007 AIME I (Problems • Resources) | ||
| Preceded by Problem 2 | Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
