I am taking linear algebra. The question asks me to express in the form a+ib for the following
1) -1(i-1)
2) i^5
3) i^n
4) (1+i)^2
5) (i^3(1+i)^5)/(1+6)^6
6) (i(i^2)(i^3)..(i^n))/(i(i^3)(i^5)..(i^(2n+1)))

Please any help would be greatly appreciated. Also, if possible please explain or write out the work so I know how to get the answer. Thank you so much

Question

I am taking linear algebra. The question asks me to express in the form a+ib for the following
1)  -1(i-1)
2) i^5
3) i^n
4) (1+i)^2
5) (i^3(1+i)^5)/(1+6)^6
6) (i(i^2)(i^3)..(i^n))/(i(i^3)(i^5)..(i^(2n+1)))

Please any help would be greatly appreciated. Also, if possible please explain or write out the work so I know how to get the answer. Thank you so much

anonymous · Answer

1)  -1(i-1) = 1 - i

anonymous · Answer

now how do i express it in the form a+ib, is it (1)+i(-1)?

anonymous · Answer

Recognize that a = constant, b is the imaginary part!

anonymous · Answer

a = 1, b = -1 => 1 - i

anonymous · Answer

okay, i wasn't sure if i was doing this properly

anonymous · Answer

For example
$$
i^2 = -1\
i^3= -i\
i^4= 1\
i^5= i = 0 +1 i\
$$