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    1.)The complex number u satisfies the equation, Solve this equation for u, expressing your answer in the form a + bi where a and b are real.
    ((u-i)/(u+1))=i
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    (Original post by sammy3000)
    1.)The complex number u satisfies the equation, Solve this equation for u, expressing your answer in the form a + bi where a and b are real.
    ((u-i)/(u+1))=i
    Multiply through by the denominator and let u = a+bi Equate real and imaginary coefficients, simultaneous equations.
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    ( u-i)/(u+1)-(i(u-i))/(u+1)=0 this is what i done but i think its wrong
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    (Original post by sammy3000)
    ( u-i)/(u+1)-(i(u-i))/(u+1)=0 this is what i done but i think its wrong
    Right so you have

    \frac{u-i}{u+1} = i Multiply both sides by u+1 and you get u-i = (u+1)i Now let u = a+bi and equate real and imaginary coefficients
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    i got u=2i/(1-i), then convert that into the form a + bi
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    (Original post by sammy3000)
    ( u-i)/(u+1)-(i(u-i))/(u+1)=0 this is what i done but i think its wrong
    So follow the advice you were given?
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    i dont really know how to Equate real and imaginary coefficients. But i got the answers the other way and I got u=i-1. But how would you do it by Equating real and imaginary coefficients.
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    (Original post by sammy3000)
    i dont really know how to Equate real and imaginary coefficients. But i got the answers the other way and I got u=i-1. But how would you do it by Equating real and imaginary coefficients.
    If a, b, c, d are real and a+bi = c+di then a=c and b=d
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    (Original post by sammy3000)
    i dont really know how to Equate real and imaginary coefficients. But i got the answers the other way and I got u=i-1. But how would you do it by Equating real and imaginary coefficients.
    That isn't right.

    Equating coefficients just means if a+bi=3+2i then a=3 and b=2.
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    (Original post by davros)
    If a, b, c, d are real and a+bi = c+di then a=c and b=d
    Och! You won that time.
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    (Original post by sammy3000)
    i dont really know how to Equate real and imaginary coefficients. But i got the answers the other way and I got u=i-1. But how would you do it by Equating real and imaginary coefficients.
    Well, if you've got a complex number z = a + bi the real coefficient is Re(z) = a and the imaginary coefficient is Im(z) = b and these are completely independent of each other. What this means is, if you've got another imaginary number p = c + di, then z = p if and only if Re(z) = Re(p) and Im(z) = Im(p) which boils down to being if and only if a = c and b = d
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    (Original post by Mr M)
    Och! You won that time.
    on speed or generality?
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    (Original post by davros)
    on speed or generality?
    Speed and mentioning the real condition.
 
 
 
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