Expressing “difficult” with 难 and 复杂
The adjectives 难 and 复杂 are translated in the same way: "complicated" or "difficult" but we should use them in different contexts.
The adjective 复杂
We use the adjective 复杂 
to emphasize that what is being talked about consists of a large number of elements. It could be a process, something with many parts, or a system.
to emphasize that what is being talked about consists of a large number of elements. It could be a process, something with many parts, or a system.Examples
这是个复杂系统，但肯定有所改进
It's a complex system, but there have definitely been improvements
zhè shì ge fùzá xìtǒng, dàn kěndìng yǒusuǒ gǎijìn
这是一本复杂却能引发兴趣的书
It is a complex but interesting book
zhè shì yì běn fùzá què néng yǐnfā xìngqù de shū
结构复杂的机器
This is a complex machine
jiégòu fùzá de jīqì
The adjective 难
We use the adjective 难 to emphasize that something is difficult for a person to do or to understand because it requires a lot of effort.
to emphasize that something is difficult for a person to do or to understand because it requires a lot of effort.Examples
这场考试相当难
This exam is quite difficult
zhè cháng kǎoshì xiāngdāng nán
毕业生感到找工作越来越难
It's getting harder and harder for graduates to find jobs
bìyèshēng gǎndào zhǎo gōngzuò yuèláiyuè nán
辨认你的笔迹有点难
It's a little hard to identify your handwriting
biànrèn nǐ de bǐjī yǒudiǎn nán
难 as an adverb
Sometimes 难 can also be an adverb meaning "difficult". In this case, it should be followed by a verb.
Pay attention
We can not use 复杂 in that way.
Examples
这个舞蹈动作很难做
This dance move is difficult to do
zhè ge wǔdǎo dòngzuò hěn nán zuò
很难解释清楚什么原因使他如此走红
It's hard to explain what made him so popular
hěn nán jiěshì qīngchu shénme yuányīn shǐ tā rúcǐ zǒuhóng
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