Question

Determine the fourth roots of 16 in the form x+iy, where x and y are not trigonomentric functions. It counts 18 marks. Where do I begin?

Answer 1

make a circle

Answer 2

since \(2^4=16\) you have one root right away, namely \(2\)
then divide the circle up in to 4 equal parts, one of them being at \(2\)

Answer 3

those are your roots,
of course we could do it with algebra as well\[x^4=16\\
x^4-16=0\\
(x^2+4)(x^2-4)=0\\
(x^2+4)(x+2)(x-2)=0\]

Answer 4

Wow. Thank you. And that really counts 18 marks? :)

Answer 5

i don't know, it is not my question
hope the answers are clear