1988 AIME Problems/Problem 11
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Problem
Let 
be complex numbers. A line 
in the complex plane is called a mean line for the points if contains points (complex numbers) 
such that
For the numbers 
, 
, 
, 
, and 
, there is a unique mean line with 
-intercept 3. Find the slope of this mean line.
Solution
Each 
lies on the complex line 
, so we can rewrite this as
Matching the real parts and the imaginary parts, we get that 
and 
. Simplifying the second summation, we find that 
, and substituting, the answer is 
.
See also
| 1988 AIME (Problems • Resources) | ||
| Preceded by Problem 10 | Followed by Problem 12 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
