Question

20．設(shè)復(fù)數(shù)$z=\frac{2i}{cos120°+isin120°}$，則|z|=（　�。�

• A． $\frac{1}{2}$
• B． $\frac{{\sqrt{3}}}{2}$
• C． 1
• D． 2

Answer 1

分析 根據(jù)復(fù)數(shù)的運(yùn)算求出z，從而求出z的模即可．

解答 解：$z=\frac{2i}{cos120°+isin120°}$
=$\frac{2i（cos120°-isin120°）}{（cos120°+isin120°）（cos120°-isin120°）}$
=2sin120°+2cos120°i
=$\sqrt{3}$-i，
則|z|=$\sqrt{3+1}$=2，
故選：D．

點(diǎn)評(píng) 本題考查了復(fù)數(shù)求模問(wèn)題，考查三角函數(shù)以及復(fù)數(shù)的運(yùn)算，是一道基礎(chǔ)題．