Which of the following is equivalent to the complex number i^{34}
choose 1
(choice a) 1
(choice b) i
(choice c) -1
(choice d) -i

Choice C, -1

Step-by-step explanation:

The trick here is to look at this as a pattern.

is i to the 1st power.

is i to the 2nd power.

is i to the 3rd power.

is i to the 4th power.

So what we do to solve something like this is divide the power by 4, and see how far away the number is from the pattern.

In other words, we divide, and our remainder is how many powers to count up to (a remainder of 0 is the 4th power).

So 34/4 = 8 with a remainder of 2. Therefore, it's i to the 2nd power, which is -1.