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# Complex Numbers help. FP1 watch

1. I'm doing a question but am stuck on one bit.

Z1= P+2i
Z2= 1-2i

Part (a) says find Z1/Z2.

I got

(P+2i)/(1-2i) x (1+2i)/(1+2i) = (P-4)/5 +(2P+2)I/5

Part (b): |z1/z2| = 13, find the possible values of P

So, Done a long way but ended up with the correct answer (+/- 29). And I went on google and wrote 'FP1 June 2014 answers' and I found Arsey's model answers.

He done the same thing as me for part A, but for part B he done 2 different methods, the one i done and another one.
It was

(p^2 + 4)/(1 + 4) = 169
(P^2 + 4) = 845
P^2 = 841
P = +/- 29

Now this way is much quicker, but i don't understand where the (p^2 + 4) came from?

Can someone please tell me where he got it from?
2. (Original post by Economistician)
I'm doing a question but am stuck on one bit.

Z1= P+2i
Z2= 1-2i

Part (a) says find Z1/Z2.

I got

(P+2i)/(1-2i) x (1+2i)/(1+2i) = (P-4)/5 +(2P+2)I/5

Part (b): |z1/z2| = 13, find the possible values of P

So, Done a long way but ended up with the correct answer (+/- 29). And I went on google and wrote 'FP1 June 2014 answers' and I found Arsey's model answers.

He done the same thing as me for part A, but for part B he done 2 different methods, the one i done and another one.
It was

(p^2 + 4)/(1 + 4) = 169
(P^2 + 4) = 845
P^2 = 841
P = +/- 29

Now this way is much quicker, but i don't understand where the (p^2 + 4) came from?

Can someone please tell me where he got it from?
(a+bi)(a-bi) = a2 + b2
3. (Original post by TeeEm)
(a+bi)(a-bi) = a2 + b2
Sorry, I don't understand. I see how that works in essence, but how did he know he had to use p+2i and p-2i?
4. (Original post by Economistician)
Sorry, I don't understand. I see how that works in essence, but how did he know he had to use p+2i and p-2i?
I have not read the question but simply he "conjugated" the denominator in order to process the algebra.
5. (Original post by TeeEm)
I have not read the question but simply he "conjugated" the denominator in order to process the algebra.
http://www.physicsandmathstutor.com/...-maths-papers/
its the first question on the one that says "Edexcel FP1 - June 2014 Model Answers by Arsey.pdf"
6. correction to what I said previously as I could not see the question.

|z1/z2| =|z1|/|z2|

now
the modulus of z1 is the square root of of p2 + 22 = p2+4
the modulus of z2 is the square root of of 12 + (-2)2 = 5

squaring the fraction = 132

....
7. (Original post by TeeEm)
correction to what I said previously as I could not see the question.

|z1/z2| =|z1|/|z2|

now
the modulus of z1 is the square root of of p2 + 22 = p2+4
the modulus of z2 is the square root of of 12 + (-2)2 = 5

squaring the fraction = 132
....
Thank you, really appreciate it.
8. (Original post by Economistician)
Thank you, really appreciate it.
no worries

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