Difference between revisions of "1991 AHSME Problems/Problem 18"
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− | We want <math>(3+4i)z</math> a real number, so we want the <math>4i</math> term to be canceled out. Then, we can make <math>z</math> be in the form <math>(n-\frac{4}{3}ni)</math> to make sure the imaginary terms cancel out when it's multiplied together. <math>(n-\frac{4}{3}ni)</math> is a line | + | We want <math>(3+4i)z</math> a real number, so we want the <math>4i</math> term to be canceled out. Then, we can make <math>z</math> be in the form <math>(n-\frac{4}{3}ni)</math> to make sure the imaginary terms cancel out when it's multiplied together. <math>(n-\frac{4}{3}ni)</math> is a line, so the answer is <math>\textbf{(D) } line</math> |
== See also == | == See also == |
Revision as of 18:53, 11 October 2016
Problem
If is the set of points
in the complex plane such that
is a real number, then
is a
(A) right triangle (B) circle (C) hyperbola (D) line (E) parabola
Solution
Solution 1:
We want a real number, so we want the
term to be canceled out. Then, we can make
be in the form
to make sure the imaginary terms cancel out when it's multiplied together.
is a line, so the answer is
See also
1991 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.