As others have said, signed languages can be at least as complex as spoken languages, and potentially much more complex given the ability to communicate multiple things simultaneously and depict actions in 3D.
For example, while watching a signed translation of the book My First Peek-a-boo Animals by Eric Carle, I saw a fluent ASL signer sign tree with one hand and then the other to depict two trees, and then turn one hand into a movement classifier to depict an animal swinging from the location she'd signed the first tree and land on the arm that was still signing the second tree. What a vivid and descriptive way to communicate "this animal swings from tree to tree"!
Regarding writing, real-life signed languages usually borrow their writing system from spoken languages, and a lot of people erroneously think it's impossible to write sign languages, but it's totally possible. There are several phonetic writing systems available for signed languages - for example, Sutton SignWriting and Stokoe notation are two such systems. None have gotten widespread use for cultural context reasons, mainly because Deaf people are a minority group who will need to learn to read and write in a manner understandable to the surrounding hearing majority, and also because access to video recording has predated writing for signed languages. But in a society where spoken language isn't used, it'd be very different.
In fact, writing might even be easier for a signing culture to invent. After all, the earliest forms of writing were pictographs. In the written forms of many spoken languages, pictographs depicting various things ended up associated with sounds present in the words for those things, eventually leading to syllabics, alphabets or abugidas. (Chinese is a notable exception for sticking to pictographs, possibly because they were writing for an empire full of mutually unintelligible languages, many of them logographic and tonal.) The earliest writing for a signing society might also be pictographic, but instead of having to draw the meaning, they could literally draw what someone signing that word looks like.
Over time, the drawings will become so stylized that an untrained reader couldn't even tell what they originally represented, just like most people nowadays don't look at 'A' and think of an antelope. However, the connection between meaningful parameters of the signs and distinct symbols in the resulting text would be retained and learnable.
I mentioned sign parameters above. They're basically the sign language equivalent to phonemes. But whereas phonemes are single, sequentially produced sounds, sign parameters come in five types - handshape, location of hand, movement of hand, orientation of hand, and nonmanual markers (communicative signals made with other body parts besides the hands, such as a pursed lip and furrowed brow to signal that you're asking an open-ended question.
Not all of these parameters necessarily have to be written, just as we don't necessarily have to indicate tone of voice or vocal emphasis when writing most spoken languages, but in cases where it's essential to understand the meaning of a statement, they'll probably mark it some way. For example, in ASL you might lose some nuance by not recording facial expressions, but you don't actually need to know they furrowed their brow and pursed their lips to know that "you name what" is an open-ended question. Or, some parameters might end up being treated more like their equivalent to punctuation rather than letters. There are a lot of ways to approach this, depending on the specific language and culture of your aliens.
One thing is certain - if they're high-tech, they will undoubtedly have multiple ways to digitize their language to communicate long-distance, including new communication methods that only work with technological assistance, such as how many people in our world communicate online with meme pictures. It'd be fascinating to think of how such technology would combine with a sign-centric linguistic culture.