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Need help with complex numbers

So I did the question and got 9 as my mod and 60 degrees as my arg but i noticed that the marking scheme had other answers as well

where the modulus is 2 and the arg -30 degrees
where the modulus is 18 and the arg is 30 degrees

I was wondering how those answered were obtained.
In my working I tried doing it by dividing out my 4.5 in my equation (4.5+4.5root3i) and i got 1+root3i which gave me the modulus 2 but my argument remained the same.
because it was still tan inverse of root 3.

Could anyone explain this?
Please and thanks :smile:
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Reply 1
Avatar for joostan
joostan
13
Original post by diannekwene
So I did the question and got 9 as my mod and 60 degrees as my arg but i noticed that the marking scheme had other answers as well

where the modulus is 2 and the arg -30 degrees
where the modulus is 18 and the arg is 30 degrees

I was wondering how those answered were obtained.
In my working I tried doing it by dividing out my 4.5 in my equation (4.5+4.5root3i) and i got 1+root3i which gave me the modulus 2 but my argument remained the same.
because it was still tan inverse of root 3.

Could anyone explain this?
Please and thanks :smile:


The ultimate answer is the same, the mark scheme simply offers another way of calculating it.
Original post by diannekwene
So I did the question and got 9 as my mod and 60 degrees as my arg but i noticed that the marking scheme had other answers as well

where the modulus is 2 and the arg -30 degrees
where the modulus is 18 and the arg is 30 degrees

I was wondering how those answered were obtained.
In my working I tried doing it by dividing out my 4.5 in my equation (4.5+4.5root3i) and i got 1+root3i which gave me the modulus 2 but my argument remained the same.
because it was still tan inverse of root 3.

Could anyone explain this?
Please and thanks :smile:


There are 2 ways to approach this question:
1. Do what you did, writing the number in the form a + ib, and then find the modulus and argument.

2. Find the modulus and argument of the top and the bottom separately and then combine these using the correct rules to get the final answer.

The other moduli and arguments that are worrying you are the half way stage of version 2. They are not alternative answers.
Reply 3
Avatar for diannekwene
diannekwene
OP
1
Original post by tiny hobbit
There are 2 ways to approach this question:
1. Do what you did, writing the number in the form a + ib, and then find the modulus and argument.

2. Find the modulus and argument of the top and the bottom separately and then combine these using the correct rules to get the final answer.

The other moduli and arguments that are worrying you are the half way stage of version 2. They are not alternative answers.


As a year 13 student, should I know how to work out the equation using the second method?
Reply 4
Avatar for diannekwene
diannekwene
OP
1
Original post by joostan
The ultimate answer is the same, the mark scheme simply offers another way of calculating it.



I wanted to know how to do the second method as well, just in case a question specifies what method to use.
Reply 5
Avatar for joostan
joostan
13
Original post by diannekwene
I wanted to know how to do the second method as well, just in case a question specifies what method to use.


The other method was to calculate the modulus and argument of the denominator and numerator separately and then combine to give the required result, using the appropriate rules.
Reply 6
Avatar for diannekwene
diannekwene
OP
1
Original post by joostan
The other method was to calculate the modulus and argument of the denominator and numerator separately and then combine to give the required result, using the appropriate rules.


Cool thank you :smile:
Reply 7
Avatar for joostan
joostan
13
Original post by diannekwene
Cool thank you :smile:


No problem. :smile:

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