Question

Can someone walk me through this?
please!

Given a= i+i^3+i^5+i^7+....,which of the
following represents a if the last term in the
series is i^41 ?
a. i
b. -i
c. 0
d. 1
e. -1

Answer 1

You can reduce the exponents of the imaginary unit modulo 4.

Answer 2

what do you mean "imaginary unit modulo 4."

Answer 3

$$n=n+4$$ In the ring of integers modulo 4

Answer 4

I am sorry but i was not taught that way so I dont know what your talking about

Answer 5

ok, you know what 'i' is ?

Answer 6

yes. but its beeen a while

Answer 7

ok, \(\large i= \sqrt{-1}\)
so, what about i^2 =... ?

Answer 8

-1

Answer 9

correct! i^2 = -1
what about i^4 = (i^2)^2 =... ?

Answer 10

1