複數計算（1+√3i)^100+(1-√3i)^100=?

題目：

複數計算（1+√3i)^100+(1-√3i)^100=?
（1加根號3乘以i）的100次方加上（1減去根號3乘以i）的一百次方=?,i是在根號3外面的

解答：

1+√3i=2(cosπ/3+sinπ/3)
1-√3i=2[cos(-π/3)+sin(-π/3)]
所以原式=2^100[cos(100π/3)+sin100π/3+cos(-100π/3)+sin(-100π/3)]
=2^100*2cos100π/3
=-2^100