Join TSR now and get all your revision questions answeredSign up now
    • Thread Starter
    Offline

    0
    ReputationRep:
    So I am doing FP1 and I understand all of it besides Loci. Question 2 from the paper can be used as an example. I know that the |a| is 5 because [(3^2+4^2)^1/2] but i don't understand arg(a) and any of 2(ii).
    Attached Images
  1. File Type: pdf 57758-question-paper-unit-4725-further-pure-mathematics-1.pdf (31.4 KB, 58 views)
    Offline

    3
    ReputationRep:
    (Original post by mhamzan786)
    So I am doing FP1 and I understand all of it besides Loci. Question 2 from the paper can be used as an example. I know that the |a| is 5 because [(3^2+4^2)^1/2] but i don't understand arg(a) and any of 2(ii).
    The argument of a complex number is the angle in radians from the positive real axis to the point on the Argand diagram. It's anti-clockwise positive.

    Now a here is in the first quadrant so \arg(a) = \tan^{-1} \frac{4}{3} = 0.927^c to three decimal places.

    |z-a|=|a| is a circle with centre a and radius |a| which you said you found. It means "all the complex numbers z on the Argand diagram that are exactly |a| away from a."

    \arg(z-3) = \arg(a) is a half-line. It means roughly "all the complex numbers z on the Argand diagram that, when you minus 3 from them, have the same argument as a does."

    I've written about it in more detail on my website here: https://www.furthermathstutor.co.uk/...x-numbers.html
 
 
 
Poll
How are you feeling about your A-level results?

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.