Difference between revisions of "1974 AHSME Problems/Problem 17"
(Created page with "==Problem== If <math> i^2=-1 </math>, then <math> (1+i)^{20}-(1-i)^{20} </math> equals <math> \mathrm{(A)\ } -1024 \qquad \mathrm{(B) \ }-1024i \qquad \mathrm{(C) \ } 0 \qquad ...") |
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==See Also== | ==See Also== | ||
{{AHSME box|year=1974|num-b=16|num-a=18}} | {{AHSME box|year=1974|num-b=16|num-a=18}} | ||
| + | [[Category:Introductory Algebra Problems]] | ||
Revision as of 09:19, 30 May 2012
Problem
If 
, then 
equals
Solution
Notice that 
and 
. Therefore,
![\[(1+i)^{20}-(1-i)^{20}=(2i)^{10}-(-2i)^{10}=(2i)^{10}-(2i)^{10}=0, \boxed{\text{C}}.\]](http://latex.artofproblemsolving.com/d/8/b/d8b4614dacf145619557236b885e0e759c1d61a5.png)
See Also
| 1974 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
| 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 | ||
