2

Part of 2009 AIME Problems

Problems(2)

Complex Fraction

Source: AIME 2009I Problem 2

There is a complex number

z

with imaginary part

164

and a positive integer

n

such that \frac {z}{z \plus{} n} \equal{} 4i. Find

n

AMCAIMEanalytic geometryrotationcomplex numbersgeometrysimilar triangles

Logarithm Exponents

Source: AIME 2009II Problem 2

a

b

c

are positive real numbers such that a^{\log_3 7} \equal{} 27, b^{\log_7 11} \equal{} 49, and c^{\log_{11} 25} \equal{} \sqrt {11}. Find a^{(\log_3 7)^2} \plus{} b^{(\log_7 11)^2} \plus{} c^{(\log_{11} 25)^2}.

logarithmsAIMEalgebra