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Complex Numbers help. FP1

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?
Reply 1
Avatar for TeeEm
TeeEm
19
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
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?
Reply 3
Avatar for TeeEm
TeeEm
19
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.
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/a-level-maths/model-answers-june-2014-maths-papers/
its the first question on the one that says "Edexcel FP1 - June 2014 Model Answers by Arsey.pdf"
Reply 5
Avatar for TeeEm
TeeEm
19
Original post by Economistician


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

....
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.
Reply 7
Avatar for TeeEm
TeeEm
19
Original post by Economistician
Thank you, really appreciate it.


no worries
Reply 8
Avatar for Asim Jay
Asim Jay
2
He is simply squaring both sides.
Reply 9
Avatar for davros
davros
16
Original post by Asim Jay
He is simply squaring both sides.

You're a bit late - this thread was answered 6 years ago :biggrin:

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