(Question 3 (a) from the CSSA trial)
question was something like find values of x if x is real and (x + i)^4 is imaginary.
here's what I did:
= x^4 + 4x^3i + 6x^2i^2 + 4xi^3 + i^4
= x^4 - 6x^2 + 1 + i(4x^3 - 4x) -> imaginary, real part = 0
ie x^4 - 6x^2 + 1 = 0
using the quadtratic formula,
x^2 = (6 +/- sqrt(32)) / 2
x^2 = 3 +/- 2sqrt(2)
x = +/- sqrt(3 +/- 2sqrt(2))
(I then wrote out the 4 answers.)
teacher's response, on the exam, was: "this should work & I can't find your mistake!"
I can't see the mistake either...
question was something like find values of x if x is real and (x + i)^4 is imaginary.
here's what I did:
= x^4 + 4x^3i + 6x^2i^2 + 4xi^3 + i^4
= x^4 - 6x^2 + 1 + i(4x^3 - 4x) -> imaginary, real part = 0
ie x^4 - 6x^2 + 1 = 0
using the quadtratic formula,
x^2 = (6 +/- sqrt(32)) / 2
x^2 = 3 +/- 2sqrt(2)
x = +/- sqrt(3 +/- 2sqrt(2))
(I then wrote out the 4 answers.)
teacher's response, on the exam, was: "this should work & I can't find your mistake!"
I can't see the mistake either...
