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# FP1 Complex watch

1. 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
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.

2. (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
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.

right

you know the value of

so expand out and equate real and imaginary parts
3. (Original post by boner in jeans)
right

you know the value of

so expand out and equate real and imaginary parts
do you mean:

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

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

right,

so

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

right,

so

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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