tongjangeul jibe dugo waseo gyejwa beonhoreul memojange jeogeo dwosseo.

Not exactly.

• 통장 usually means a bankbook / passbook in Korean.
• It refers to the physical booklet or bankbook connected to an account.
• 계좌 is the account itself.

So in this sentence:

• 통장 = the physical bankbook
• 계좌 번호 = the account number

That is why both can appear in the same sentence without being redundant.

두고 오다 literally means to leave something somewhere and come back / come away.

It is made of:

• 두다 = to put, leave
• 오다 = to come

So 통장을 집에 두고 왔어 means:

• I left the bankbook at home and came here
• or more naturally, I left my bankbook at home

The 오다 part adds the idea that the speaker is now somewhere else after leaving it there.

Because 두고 와서 gives a more specific situation.

• 두어서 would just mean because I left/put it
• 두고 와서 means because I left it there and came away

That extra 오다 makes the situation more vivid and natural in Korean when you are talking about having left something behind at another place.

놓고 오다 is also possible in many situations, but 두고 오다 is very common for leaving something behind somewhere.

Here, -아서 / -어서 connects the two actions and gives a reason/background relationship.

• 통장을 집에 두고 와서
• 계좌 번호를 메모장에 적어 뒀어

This means something like:

• Since/Because I left the bankbook at home, I wrote down the account number in my memo pad.

So the first clause explains why the second action was done.

It can also sometimes just connect actions in sequence, but here the reason meaning is the natural one.

They are related, but they mark different kinds of location.

• 집에 = at home / to home
  Here it marks the place where the bankbook was left.
• 메모장에 = in/on the memo pad
  Here it marks the place where the account number was written.

So both are location-related, but:

• 집에 두다 = leave something at home
• 메모장에 적다 = write something in/on a memo pad

Korean often uses 에 where English might use at, in, on, or to.

Because it is the direct object of 적다.

• 계좌 번호를 적다 = to write down the account number

The thing being written gets 을/를.

So:

• 계좌 번호를 = the account number
• 메모장에 적어 뒀어 = wrote it down in the memo pad and kept it there for later use

적어 뒀어 is a contraction of 적어 두었어.

• 적다 = to write
• -아/어 두다 = to do something and leave it that way / do it in preparation for later

So:

• 적었어 = I wrote it
• 적어 뒀어 = I wrote it down and kept it there for later / I made a note of it

This form often implies:

• preparation
• convenience for future use
• keeping a result in place

In this sentence, 적어 뒀어 sounds very natural because the speaker wrote down the account number so they could use it later after leaving the bankbook at home.

Yes.

뒀어 is the contracted spoken form of 두었어.

So:

• 적어 두었어 → more full form
• 적어 뒀어 → common contracted form in speech

Both mean the same thing, but 뒀어 sounds more natural in everyday conversation.

Because Korean often omits the subject when it is clear from context.

In English, you usually need to say I:

• I left my bankbook at home, so I wrote down the account number in my memo pad.

In Korean, if the speaker is obviously talking about themselves, the subject can be left out:

• 통장을 집에 두고 와서 계좌 번호를 메모장에 적어 뒀어.

The listener naturally understands the subject as I from context.

It is casual informal speech.

This style is used:

• with close friends
• with younger people
• in diary-like self-talk
• in casual conversation

A more polite version would be:

• 통장을 집에 두고 와서 계좌 번호를 메모장에 적어 뒀어요.

And a less contracted, slightly more formal-sounding version could be:

• 통장을 집에 두고 와서 계좌 번호를 메모장에 적어 두었어요.

It can be either, depending on context.

메모장 can refer to:

• a physical memo pad / notepad
• a memo app on a phone or computer

Without extra context, Korean does not force one interpretation here. Native speakers would usually figure it out from the situation.

The order is somewhat flexible, but this version is very natural.

Current order:

• 통장을 집에 두고 와서
• 계좌 번호를 메모장에 적어 뒀어

This gives a clear flow:

1. background/reason
2. resulting action

You can move some parts around, especially objects and location phrases, but this order sounds natural because it presents the cause first and the response second.

For example, Korean allows some rearrangement, but the original sentence is a very normal way to say it.