dw, it takes a long time to get your head around the subject initially. like for me it probably took two terms or more, but really got a handle on it around trials.
complex geo is probably one of the hardest parts of the syllabus, next to proofs. the easier parts of the syllabus are some parts of vectors, mechanics and integration. integration is fairly standard after you've done the exercises and warmed up, mechanics is basically just integration (the hardest part is setting out the question, and since you do physics, this will make it easier for you), the easy parts of vectors are basically 3u vectors. my school started out on complex numbers and proofs from memory, so of course it was going to be tough, but this was actually the best way to do things since you had a long time to practice these difficult topics.
the reason why complex and proofs are so hard is because these are the first times in a math subject that you can't just rote learn 90% of the questions. even 3u has a lot of areas that you can do well in through knowing the procedure well, though some questions can be difficult. in comparison, 4u is much more abstract, and (at least for complex and proofs) it's entirely possible for every question to have a different approach. the only way to improve at this is hitting your head against the wall for ages, until something clicks (you also need to be smart about your approach later, but since you're starting out, the only way to get started is exposure). at least for me, this was true for most of my subjects in high school, hard subjects at uni, and also for a research project that i'm doing at uni right now. all i can say is that, if you're planning to study anything with "problem solving" in the future, you're most likely going to hit a similar roadblock.
if you're finding complex geo to be hard i can at least recommend to do these things:
- do as many questions as possible, starting with the textbook and going through trial/exam papers later. you can't say that you're bad at the topic, unless if you've done this, as this is the bare minimum to accumulate skill (even if this takes time to begin with)
- if you're finding it conceptually hard, ask yourself why. personally, i never got taught geometry in years 7-10, or at least not in very good detail. so i didn't know what a quadrilateral was, what a rhombus was, what an arc was, any circle geometry etc. to fix this i compiled all the properties in a page, so anytime i was doing a question involving parallelograms i could check the properties, or if there was something involving circles i'd at least know the theorems about radius is at right angle to the tangent etc. it might just be that you're missing earlier knowledge, and so you can't progress without fixing this. if it's to do with specifically geometry of complex numbers, it's helpful to just think of them as vectors or points in 2d space, with special multiplication. oftentimes, complex geo questions can be done using complex methods, or you can just convert them into vector problems. also, note the similarity of a lot of questions. i always struggled with the max/min argument type questions, but after a while you notice the main pattern and can solve the majority of questions (i forgot how to do them now though)
- don't spend too long on the proof, and peek at the solution and try to finish it. i still do this now if working through a textbook, if i spend 1+ hour (or even 30 minutes if i'm completly clueless) on a problem i lookup the solution. but don't just copy it because this is useless, instead see what idea they used and try to figure it out yourself. especially if you've never seen the type of problem before, or never seen anyone write a proof on the topic, you might just be unable to start and you endup wasting time. personally when self learning, i had to do this a lot, especially because there's no exposure to seeing how someone approaches the problem
just know that things will get easier as you familiarise with the subject. besides that, the topics you struggle the most will eventually get watered down with the topics that you're good at, another reason why 4u gets easier as time goes on. the first assessment tasks can be the worst, as they're on 1-2 topics and test every little detail. by the time you hit trials, you don't necessarily need complete mastery of every dot point to get a decent mark as long as you have a firm understanding of the basics behind each topic. this also gives you much more energy to focus on those weak areas, as you're not constantly having to spend hours on a problem and worrying about if you being able to solve it will be make or break
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