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?
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?