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1. 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
2. (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 Equate real and imaginary coefficients, simultaneous equations.
3. ( u-i)/(u+1)-(i(u-i))/(u+1)=0 this is what i done but i think its wrong
4. (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

Multiply both sides by u+1 and you get Now let and equate real and imaginary coefficients
5. i got u=2i/(1-i), then convert that into the form a + bi
6. (Original post by sammy3000)
( u-i)/(u+1)-(i(u-i))/(u+1)=0 this is what i done but i think its wrong
7. 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.
8. (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
9. (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 then a=3 and b=2.
10. (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.
11. (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 the real coefficient is and the imaginary coefficient is and these are completely independent of each other. What this means is, if you've got another imaginary number , then if and only if and which boils down to being if and only if and
12. (Original post by Mr M)
Och! You won that time.
on speed or generality?
13. (Original post by davros)
on speed or generality?
Speed and mentioning the real condition.

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