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    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).
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    (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
 
 
 
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