Further Maths help

Soldato
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I'm not sure who has got this answer right, me or my textbook (it wouldn't be the first time it gets something wrong).

This is imaginary numbers btw, i = square root of -1.

Q10. Given that z = -1 + 3i, express z + 2/z in the form a + ib, where a,b € R (a and b belong to the set of real numbers).

This is what I did:

z + 2/z

(-1 + 3i) + 2/(-1 + 3i)

(-1 + 3i) (-1 + 3i) + 2

Expand the brackets: 1 - 6i + 9(i squared)

1 - 6i - 9 -> -8 - 6i

-8 - 6i + 2 -> -6 - 6i

The book's answer is: -6/5 (1 - 2i)

Have I just made some retarded mistake or is their answer wrong?
 
I'm not sure who has got this answer right, me or my textbook (it wouldn't be the first time it gets something wrong).

This is imaginary numbers btw, i = square root of -1.

Q10. Given that z = -1 + 3i, express z + 2/z in the form a + ib, where a,b € R (a and b belong to the set of real numbers).

This is what I did:

z + 2/z

(-1 + 3i) + 2/(-1 + 3i)

(-1 + 3i) (-1 + 3i) + 2

First of all, shouldn't this be:

((-1 + 3i) (-1 + 3i) + 2)/(-1 + 3i)?

I.E. the second expression all over -1 + 3i.

You cross multiply and multiply the denominators when adding fractions right? I think... :confused:
 
Yeah, Beenom is right.
What you've done is you've multiplied up by (-1 +3i) but it doesn't quite work like that unless you are solving an equation (i.e. you have an equals sign in there somewhere and you can do the same to both sides).
I haven't done the calculation, but if you take the answer you got and divide it by (-1 +3i) do you get the same answer as in the book?
 
You need to multiply the numerator and denominator of the fraction 2/z by z* (z's conjugate):

2/z
= 2z*/zz*
= 2(-1 - 3i)/(-1 + 3i)(-1 - 3i)
= -2(1 + 3i)/(1 + 9)

= -(1 + 3i)/5

You can do the rest from there :)
 
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