返回题库

HMMT 二月 2009 · 冲刺赛 · 第 21 题

HMMT February 2009 — Guts Round — Problem 21

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

  1. [ 10 ] Simplify
    2 cos (ln(2009) i ) + i sin(ln(4036081) i ) .2
    12 HARVARD-MIT MATHEMATICS TOURNAMENT, 21 FEBRUARY 2009 — GUTS ROUNDth

英文原题

[ 10 ] Simplify
2 cos 2 (ln(2009) i ) + i sin(ln(4036081) i ) .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12 th HARVARD-MIT MATHEMATICS TOURNAMENT, 21 FEBRUARY 2009 — GUTS ROUND

解析

英文解析

  1. [ 10 ] Simplify
    2 cos (ln(2009) i ) + i sin(ln(4036081) i ) .2
    4036082
    Answer: Solution: We have
    4036081
    2 cos (ln(2009) i ) + i sin(ln(4036081) i ) = 1 + cos(2 ln(2009) i ) + i sin(ln(4036081) i )2 = 1 + cos(ln(4036081) i ) + i sin(ln(4036081) i )
    i ln(4036081)2 = 1 + e = 1 +1
    4036081
    4036082
    4036081=
    as desired.
    12 HARVARD-MIT MATHEMATICS TOURNAMENT, 21 FEBRUARY 2009 — GUTS ROUNDth