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    p64 FP1 Edexcel Q11


    z1 = √3 + i ... z2 = 1 - i

    part b) says to express 1/z1 and 1/z2 in the form a+ib
    this leaves the answers
    1/z1 = (√3 / 4) - ( i / 4)
    1/z2 = (1/2) + (i/2)

    part c) then says find the values of the real numbers of A and B such that:
    A/z1 + B/z2 = z1 + z2

    I'm unsure how I should approach this. I know the value of z1 + z2 will be:
    1+√3 ... but that's as far as I got.


    ----
    Q12 is also very similar. I could probably do that question if I have the right technique for this one.


    Thanks in advance
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    (Original post by Lunch_Box)
    p64 FP1 Edexcel Q11


    z1 = √3 + i ... z2 = 1 - i

    part b) says to express 1/z1 and 1/z2 in the form a+ib
    this leaves the answers
    1/z1 = (√3 / 4) - ( i / 4)
    1/z2 = (1/2) + (i/2)

    part c) then says find the values of the real numbers of A and B such that:
    A/z1 + B/z2 = z1 + z2

    I'm unsure how I should approach this. I know the value of z1 + z2 will be:
    1+√3 ... but that's as far as I got.


    ----
    Q12 is also very similar. I could probably do that question if I have the right technique for this one.


    Thanks in advance
    right

    you know the value of z_{1} + z_{2}

    so expand out \frac{A}{z_{1}} + \frac{B}{z_{2}} and equate real and imaginary parts
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    (Original post by boner in jeans)
    right

    you know the value of z_{1} + z_{2}

    so expand out \frac{A}{z_{1}} + \frac{B}{z_{2}} and equate real and imaginary parts
    do you mean:

    A(z2) + B(z1) / z1z2 ??
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    (Original post by Lunch_Box)
    do you mean:

    A(z2) + B(z1) / z1z2 ??
    sorry what?

    right, \frac{1}{z_{1}} = \frac{\sqrt{3}-i}{4} and \frac{1}{z_{2}} = \frac{1+i}{2}

    so

    \dfrac{A(\sqrt{3}-i)}{4} + \dfrac{B(1+i)}{2} = 1 + \sqrt{3}

    now can you tidy the LHS and equate real and imaginary coefficients on the LHS and RHS?
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    (Original post by boner in jeans)
    sorry what?

    right, \frac{1}{z_{1}} = \frac{\sqrt{3}-i}{4} and \frac{1}{z_{2}} = \frac{1+i}{2}

    so

    \dfrac{A(\sqrt{3}-i)}{4} + \dfrac{B(1+i)}{2} = 1 + \sqrt{3}

    now can you tidy the LHS and equate real and imaginary coefficients on the LHS and RHS?
    Got it, thanks for your help.
 
 
 
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