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Using Binomial Expansion in Further Maths

Hi, I just started my A level in further maths and have been set a question based on complex numbers.

The question is this:
By using the binomial expansion, or otherwise, show that (1+2i)^5 = 41 - 38i.

Now what is confusing me is that this question is in topic 1 of the book we're using, meaning we have not yet learned about binomial expansion.
It will probably be really obvious once someone explains it, but I have no idea how to get the the answer without confusing myself.

Any advice will be much appreciated.
Thanks
Original post by _L0z_
Hi, I just started my A level in further maths and have been set a question based on complex numbers.

The question is this:
By using the binomial expansion, or otherwise, show that (1+2i)^5 = 41 - 38i.

Now what is confusing me is that this question is in topic 1 of the book we're using, meaning we have not yet learned about binomial expansion.
It will probably be really obvious once someone explains it, but I have no idea how to get the the answer without confusing myself.

Any advice will be much appreciated.
Thanks

Binomial expansion used to be part of regular A-level maths. I would assume it’s still the case, thus they expect you to pick it up from prior knowledge. Maybe skim threw your A-level maths textbook.
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_L0z_
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Original post by mnot
Binomial expansion used to be part of regular A-level maths. I would assume it’s still the case, thus they expect you to pick it up from prior knowledge. Maybe skim threw your A-level maths textbook.

Possibly but it hasn't yet been mentioned in my A level maths class either but I will have a check.
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Pangol
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Original post by _L0z_
Possibly but it hasn't yet been mentioned in my A level maths class either but I will have a check.

Unfortunately, this is a problem you are likely to encounter in various contexts. Under the current specification, it is quite tricky to learn the regular and further maths A levels at the same time, the pure content assumes that you have already done at least the first year of the regular A level. There are some routes that make life a bit easier - which exam board are you taking?
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_L0z_
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Original post by Pangol
Unfortunately, this is a problem you are likely to encounter in various contexts. Under the current specification, it is quite tricky to learn the regular and further maths A levels at the same time, the pure content assumes that you have already done at least the first year of the regular A level. There are some routes that make life a bit easier - which exam board are you taking?

I am taking edexcel but i think i may have finally cracked the question. Thank you for your help
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Pangol
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Original post by _L0z_
I am taking edexcel but i think i may have finally cracked the question. Thank you for your help

It's a more general point rather than one just about this question. There are some further pure topics which you can study without the need for much regular A level knowledge, but another option is to study an applied module first, if you are taking one. D1 requires no foreknowledge at all, and further mechanics 1 doesn't need much. Doing one of these first gives you a chance to get a bit of the way through the regular A level.
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_L0z_
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Original post by Pangol
It's a more general point rather than one just about this question. There are some further pure topics which you can study without the need for much regular A level knowledge, but another option is to study an applied module first, if you are taking one. D1 requires no foreknowledge at all, and further mechanics 1 doesn't need much. Doing one of these first gives you a chance to get a bit of the way through the regular A level.

Thats a good idea, it might be a good idea to read into those as it could help with some of the other topics too. Although my books are chaptered in numbers so may I ask what does D1 and the applied modules consist of?
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Pangol
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Original post by _L0z_
Thats a good idea, it might be a good idea to read into those as it could help with some of the other topics too. Although my books are chaptered in numbers so may I ask what does D1 and the applied modules consist of?

The Edexcel further maths A level consists of four papers. Two are compulsory, and are made up of core pure topics from the two core pure text books. I expect it is one of these that you have. If you look on the back cover, you will see details of the other books in the series. There is one book for each module. If you are studying at a school or college, you might have some choice as to which modules you can take, but they may choose them for you.

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